Distinct representations of "zipper numbers" less than 1000.
a177196.txt - Ray Chandler (rayjchandler(AT)sbcglobal.net), May 04 2010
4 = 2^2
8 = 2^1*4^1
25 = 5^2
26 = 2^1*13^1
27 = 3^1*3^2
36 = 2^2*3^2
44 = 2^1*22^1 = 4^1*11^1
48 = 2^3*6^1 = 3^1*16^1 = 2^1*2^3*3^1 = 2^2*2^2*3^1
54 = 2^1*3^3
56 = 4^1*14^1
62 = 2^1*31^1
64 = 8^2 = 2^1*2^5 = 2^2*2^4 = 2^2*4^2 = 2^3*2^3
65 = 5^1*13^1
68 = 4^1*17^1
75 = 3^1*25^1
80 = 2^1*40^1 = 4^1*20^1
84 = 7^1*12^1
92 = 4^1*23^1
96 = 6^1*16^1 = 2^1*2^3*6^1 = 2^1*3^1*16^1 = 2^2*2^2*6^1 = 2^1*2^1*2^3*3^1 = 2^1*2^2*2^2*3^1
98 = 2^1*49^1
108 = 3^2*12^1
121 = 11^2
125 = 5^3
128 = 2^1*2^6 = 2^2*2^5 = 2^3*2^4 = 2^3*4^2 = 4^1*32^1
129 = 3^1*43^1
143 = 11^1*13^1
147 = 7^1*21^1
155 = 5^1*31^1
156 = 3^1*52^1
164 = 4^1*41^1
168 = 7^1*24^1 = 2^1*7^1*12^1 = 3^1*4^1*14^1
176 = 4^1*44^1 = 8^1*22^1 = 2^1*2^1*2^1*22^1 = 2^1*2^1*4^1*11^1
182 = 13^1*14^1
183 = 3^1*61^1
184 = 2^1*2^2*23^1
188 = 2^1*94^1 = 4^1*47^1
189 = 7^1*27^1
192 = 2^3*24^1 = 2^6*3^1 = 12^1*16^1 = 2^1*2^3*12^1 = 2^2*2^2*12^1
195 = 3^1*5^1*13^1
206 = 2^1*103^1
216 = 6^3
224 = 2^1*112^1
242 = 2^1*121^1 = 11^1*22^1
248 = 4^1*62^1 = 8^1*31^1 = 2^1*2^1*2^1*31^1
256 = 2^6*4^1 = 2^1*2^1*4^3 = 2^1*2^2*32^1
258 = 6^1*43^1 = 2^1*3^1*43^1
260 = 2^1*130^1 = 13^1*20^1
264 = 2^3*33^1 = 2^3*3^1*11^1
270 = 3^2*30^1
276 = 3^1*4^1*23^1
278 = 2^1*139^1
284 = 4^1*71^1
288 = 16^1*18^1 = 2^1*2^3*18^1 = 2^1*4^1*36^1 = 2^2*2^2*18^1 = 2^2*3^2*8^1 = 2^1*3^2*4^1*4^1 = 2^3*3^1*3^1*4^1 = 2^1*2^1*2^1*2^2*3^2
294 = 7^1*42^1 = 2^1*7^1*21^1
296 = 2^1*148^1 = 4^1*74^1
308 = 14^1*22^1
318 = 3^1*106^1
328 = 2^1*2^2*41^1
336 = 2^3*42^1 = 16^1*21^1 = 2^1*2^3*21^1 = 2^2*2^2*21^1
338 = 13^1*26^1
341 = 11^1*31^1
343 = 7^3
345 = 3^1*115^1
352 = 2^5*11^1
357 = 7^1*51^1
366 = 6^1*61^1 = 2^1*3^1*61^1
368 = 2^1*184^1 = 4^1*92^1 = 2^1*2^1*4^1*23^1
372 = 3^1*124^1
374 = 17^1*22^1
375 = 15^1*25^1
377 = 13^1*29^1
378 = 7^1*54^1 = 3^1*3^1*3^1*14^1
384 = 2^6*6^1 = 16^1*24^1 = 2^1*2^3*24^1 = 2^1*2^6*3^1 = 2^1*12^1*16^1 = 2^2*2^2*24^1 = 2^2*2^5*3^1 = 2^3*2^4*3^1 = 2^3*3^1*4^2 = 3^1*4^1*32^1 = 2^1*2^1*2^3*12^1 = 2^1*2^2*2^2*12^1
386 = 2^1*193^1
387 = 9^1*43^1
392 = 2^3*7^2
396 = 2^1*9^1*22^1 = 4^1*9^1*11^1
399 = 7^1*57^1
400 = 20^2
404 = 2^1*202^1 = 4^1*101^1
408 = 2^3*51^1 = 12^1*34^1
416 = 4^1*104^1 = 13^1*32^1
422 = 2^1*211^1
426 = 3^1*142^1
428 = 4^1*107^1
432 = 3^1*12^2
434 = 14^1*31^1
440 = 2^1*220^1 = 4^1*110^1 = 11^1*40^1 = 20^1*22^1
448 = 2^6*7^1 = 2^3*4^1*14^1
452 = 4^1*113^1
453 = 3^1*151^1
455 = 13^1*35^1
458 = 2^1*229^1
459 = 3^1*3^2*17^1
464 = 4^1*116^1
465 = 3^1*5^1*31^1
468 = 9^1*52^1 = 2^1*13^1*18^1 = 3^1*3^1*4^1*13^1
476 = 2^1*238^1 = 4^1*119^1
480 = 2^3*60^1 = 3^1*160^1 = 16^1*30^1 = 2^1*2^3*30^1 = 2^1*10^1*24^1 = 2^2*2^2*30^1 = 2^3*3^1*20^1 = 2^4*3^1*10^1 = 3^1*4^2*10^1 = 2^1*2^1*10^1*12^1
486 = 6^1*9^2 = 2^1*3^1*9^2 = 2^1*3^2*27^1 = 3^1*3^1*54^1
492 = 3^1*4^1*41^1
494 = 2^1*247^1 = 13^1*38^1
506 = 22^1*23^1
515 = 5^1*103^1
516 = 12^1*43^1
524 = 4^1*131^1
525 = 21^1*25^1
527 = 17^1*31^1
528 = 16^1*33^1 = 2^1*2^3*33^1 = 2^2*2^2*33^1 = 2^3*6^1*11^1 = 3^1*11^1*16^1 = 2^1*2^3*3^1*11^1 = 2^2*2^2*3^1*11^1
533 = 13^1*41^1
536 = 4^1*134^1
539 = 11^1*49^1
540 = 3^3*20^1
546 = 3^1*13^1*14^1
548 = 2^1*274^1 = 4^1*137^1
549 = 9^1*61^1
558 = 2^1*9^1*31^1
560 = 4^1*140^1 = 5^1*112^1 = 14^1*40^1
566 = 2^1*283^1
567 = 7^1*81^1 = 3^1*3^1*63^1 = 3^1*3^3*7^1 = 3^1*9^1*21^1 = 3^2*3^2*7^1
572 = 4^1*143^1 = 13^1*44^1 = 22^1*26^1 = 2^1*2^1*11^1*13^1
576 = 2^6*9^1 = 16^1*36^1 = 2^1*2^3*36^1 = 2^1*4^1*72^1 = 2^2*2^2*36^1 = 2^2*6^1*24^1 = 2^5*3^1*6^1 = 3^1*3^1*8^2 = 3^2*4^1*16^1 = 4^1*4^1*6^2 = 2^1*2^1*2^2*6^2 = 2^1*2^2*3^1*24^1 = 2^1*2^2*6^1*12^1 = 2^1*2^3*3^2*4^1 = 2^1*2^5*3^1*3^1 = 2^2*2^2*3^2*4^1 = 2^2*2^4*3^1*3^1 = 2^2*3^1*3^1*4^2 = 2^3*2^3*3^1*3^1 = 3^1*4^1*4^1*12^1 = 2^1*2^1*2^2*3^1*12^1
584 = 2^1*292^1 = 4^1*146^1
588 = 3^1*196^1 = 7^1*84^1 = 6^1*7^1*14^1 = 2^1*3^1*7^1*14^1
594 = 3^2*66^1 = 3^1*6^1*33^1 = 2^1*3^1*3^1*33^1 = 3^1*3^1*6^1*11^1 = 2^1*3^1*3^1*3^1*11^1
596 = 4^1*149^1
602 = 2^1*301^1
605 = 5^1*121^1
608 = 4^1*152^1
615 = 3^1*205^1
616 = 2^2*11^1*14^1
620 = 2^1*310^1 = 20^1*31^1
624 = 12^1*52^1
636 = 6^1*106^1 = 2^1*3^1*106^1
638 = 2^1*319^1 = 11^1*58^1 = 22^1*29^1
640 = 2^5*20^1 = 2^6*10^1
642 = 3^1*214^1
644 = 4^1*161^1
645 = 15^1*43^1
648 = 6^2*18^1 = 2^1*2^2*9^2 = 2^1*3^2*36^1 = 2^1*4^1*81^1 = 2^2*3^1*54^1 = 3^1*3^1*72^1 = 3^1*12^1*18^1 = 3^3*4^1*6^1 = 2^1*3^1*3^3*4^1 = 2^1*3^2*3^2*4^1 = 2^3*3^1*3^1*3^2
650 = 5^1*130^1 = 13^1*50^1
656 = 2^1*328^1 = 4^1*164^1 = 2^1*2^1*4^1*41^1
660 = 2^1*10^1*33^1 = 6^1*10^1*11^1 = 2^1*3^1*10^1*11^1
668 = 4^1*167^1
672 = 16^1*42^1 = 2^1*2^3*42^1 = 2^1*16^1*21^1 = 2^2*2^2*42^1 = 4^1*12^1*14^1 = 2^1*2^1*2^3*21^1 = 2^1*2^2*2^2*21^1
674 = 2^1*337^1
675 = 3^2*75^1 = 25^1*27^1 = 3^1*15^1*15^1 = 3^2*5^1*15^1 = 3^3*5^1*5^1
680 = 4^1*170^1 = 17^1*40^1
686 = 14^1*49^1 = 2^1*7^1*7^2
688 = 2^1*2^2*86^1
690 = 6^1*115^1 = 2^1*3^1*115^1
692 = 2^1*346^1 = 4^1*173^1
695 = 5^1*139^1
696 = 2^3*87^1 = 2^3*3^1*29^1
704 = 2^6*11^1 = 22^1*32^1
713 = 23^1*31^1
714 = 7^1*102^1 = 21^1*34^1
723 = 3^1*241^1
728 = 2^1*364^1 = 4^1*182^1 = 13^1*56^1 = 2^1*2^1*13^1*14^1
729 = 3^1*3^1*81^1 = 3^1*3^1*3^1*3^3 = 3^1*3^1*3^2*3^2
732 = 12^1*61^1
735 = 7^1*105^1
736 = 2^3*4^1*23^1
737 = 11^1*67^1
744 = 6^1*124^1 = 2^1*3^1*124^1
746 = 2^1*373^1
750 = 3^1*250^1 = 25^1*30^1
756 = 3^2*84^1 = 7^1*108^1 = 2^2*3^1*63^1 = 2^2*3^3*7^1 = 2^2*9^1*21^1 = 3^1*6^1*42^1 = 3^2*6^1*14^1 = 6^1*6^1*21^1 = 2^1*3^1*3^1*42^1 = 2^1*3^1*3^2*14^1 = 2^1*3^1*6^1*21^1 = 2^1*2^1*3^1*3^1*21^1
764 = 2^1*382^1 = 4^1*191^1
767 = 13^1*59^1
768 = 2^3*96^1 = 16^1*48^1 = 2^1*2^3*48^1 = 2^1*6^1*64^1 = 2^2*2^2*48^1 = 4^1*8^1*24^1 = 2^1*2^1*3^1*64^1 = 2^1*2^4*4^1*6^1 = 2^1*4^1*4^2*6^1 = 2^1*4^1*8^1*12^1 = 2^2*2^3*4^1*6^1 = 2^2*3^1*4^1*16^1 = 2^1*2^1*2^1*4^1*24^1 = 2^1*2^1*2^4*3^1*4^1 = 2^1*2^1*3^1*4^1*4^2 = 2^1*2^2*2^3*3^1*4^1 = 2^2*2^2*2^2*3^1*4^1 = 2^1*2^1*2^1*2^1*4^1*12^1
770 = 22^1*35^1
774 = 18^1*43^1
776 = 4^1*194^1
777 = 3^1*259^1
780 = 15^1*52^1 = 3^1*10^1*26^1 = 5^1*12^1*13^1
782 = 2^1*391^1
783 = 3^3*29^1
784 = 2^3*7^1*14^1 = 4^1*4^1*7^2 = 2^1*2^1*2^2*7^2
785 = 5^1*157^1
788 = 4^1*197^1
792 = 2^1*18^1*22^1 = 2^2*6^1*33^1 = 2^3*9^1*11^1 = 4^1*11^1*18^1 = 2^1*2^2*3^1*33^1 = 2^2*3^1*6^1*11^1 = 3^1*3^1*4^1*22^1 = 2^1*2^2*3^1*3^1*11^1
798 = 2^1*7^1*57^1 = 3^1*7^1*38^1
800 = 2^1*400^1 = 2^3*10^2 = 4^1*200^1 = 20^1*40^1
806 = 13^1*62^1 = 26^1*31^1
810 = 3^4*10^1
812 = 4^1*203^1
816 = 16^1*51^1 = 24^1*34^1 = 2^1*2^3*51^1 = 2^1*12^1*34^1 = 2^2*2^2*51^1
818 = 2^1*409^1
819 = 7^1*117^1 = 3^2*7^1*13^1
824 = 4^1*206^1 = 8^1*103^1 = 2^1*2^1*2^1*103^1
825 = 25^1*33^1 = 3^1*11^1*25^1
828 = 2^2*3^1*3^1*23^1
832 = 2^6*13^1 = 2^1*2^2*104^1
836 = 2^1*418^1 = 4^1*209^1 = 11^1*76^1 = 22^1*38^1
837 = 3^2*93^1
840 = 2^3*105^1 = 7^1*120^1 = 12^1*70^1 = 2^1*10^1*42^1 = 2^1*2^1*10^1*21^1
841 = 29^2
845 = 13^1*65^1
848 = 2^1*2^1*4^1*53^1
852 = 6^1*142^1 = 2^1*3^1*142^1
854 = 2^1*427^1
858 = 3^1*286^1
860 = 4^1*215^1
861 = 7^1*123^1
864 = 16^1*54^1 = 2^1*2^3*54^1 = 2^1*4^1*108^1 = 2^2*2^2*54^1 = 2^2*3^1*72^1 = 2^2*12^1*18^1 = 2^4*3^2*6^1 = 3^2*4^2*6^1 = 3^2*8^1*12^1 = 2^1*2^1*3^2*24^1 = 2^1*2^2*3^3*4^1 = 2^1*2^4*3^1*3^2 = 2^1*3^1*3^2*4^2 = 2^2*2^3*3^1*3^2 = 3^1*3^1*3^1*32^1 = 2^1*2^1*2^1*3^2*12^1
872 = 2^1*436^1 = 4^1*218^1
875 = 5^1*175^1
876 = 2^1*6^1*73^1 = 2^1*2^1*3^1*73^1
880 = 2^3*5^1*22^1
882 = 7^1*126^1
884 = 13^1*68^1 = 2^1*2^1*13^1*17^1
885 = 3^1*295^1
888 = 3^1*8^1*37^1 = 2^1*2^1*6^1*37^1 = 2^1*2^1*2^1*3^1*37^1
890 = 2^1*445^1
891 = 3^2*9^1*11^1
896 = 2^4*7^1*8^1 = 4^2*7^1*8^1 = 2^1*2^1*4^1*56^1 = 2^1*2^2*4^1*28^1 = 2^1*2^2*7^1*16^1 = 2^1*4^1*8^1*14^1 = 2^3*4^1*4^1*7^1 = 2^1*2^1*2^1*2^4*7^1 = 2^1*2^1*2^1*4^2*7^1 = 2^1*2^1*2^2*2^3*7^1 = 2^1*2^2*2^2*2^2*7^1 = 2^1*2^1*2^1*2^1*4^1*14^1
900 = 3^2*10^1*10^1
902 = 22^1*41^1
903 = 21^1*43^1
904 = 2^1*2^2*113^1
906 = 6^1*151^1 = 2^1*3^1*151^1
908 = 2^1*454^1 = 4^1*227^1
912 = 2^3*114^1 = 3^1*304^1
915 = 15^1*61^1
918 = 27^1*34^1 = 2^1*3^3*17^1 = 3^1*6^1*51^1 = 2^1*3^1*3^1*51^1
920 = 4^1*230^1 = 23^1*40^1
923 = 13^1*71^1
924 = 7^1*132^1 = 3^1*14^1*22^1 = 7^1*11^1*12^1
926 = 2^1*463^1
928 = 2^5*29^1
932 = 4^1*233^1
935 = 11^1*85^1
936 = 18^1*52^1 = 2^1*4^1*117^1 = 2^1*13^1*36^1 = 2^2*3^2*26^1 = 2^1*3^2*4^1*13^1 = 2^3*3^1*3^1*13^1
938 = 14^1*67^1
944 = 2^1*472^1 = 4^1*236^1
945 = 7^1*135^1 = 3^1*3^2*35^1 = 3^1*3^1*5^1*21^1
948 = 12^1*79^1
954 = 9^1*106^1
956 = 4^1*239^1
960 = 2^6*15^1 = 6^1*160^1 = 16^1*60^1 = 2^1*2^3*60^1 = 2^1*3^1*160^1 = 2^1*16^1*30^1 = 2^2*2^2*60^1 = 2^3*6^1*20^1 = 2^4*6^1*10^1 = 3^1*16^1*20^1 = 4^2*6^1*10^1 = 8^1*10^1*12^1 = 2^1*2^1*2^3*30^1 = 2^1*2^1*10^1*24^1 = 2^1*2^2*2^2*30^1 = 2^1*2^3*3^1*20^1 = 2^1*2^4*3^1*10^1 = 2^1*3^1*4^2*10^1 = 2^2*2^2*3^1*20^1 = 2^2*2^3*3^1*10^1 = 2^1*2^1*2^1*10^1*12^1
962 = 2^1*481^1 = 13^1*74^1
965 = 5^1*193^1
966 = 7^1*138^1 = 6^1*7^1*23^1 = 2^1*3^1*7^1*23^1
969 = 3^1*17^1*19^1
972 = 6^2*27^1 = 2^1*3^2*54^1 = 2^2*3^1*81^1 = 3^1*3^1*108^1 = 3^1*12^1*27^1 = 2^2*3^1*3^1*3^3 = 2^2*3^1*3^2*3^2
975 = 25^1*39^1 = 3^1*5^1*5^1*13^1
980 = 2^1*490^1 = 4^1*245^1 = 20^1*49^1
984 = 2^1*6^1*82^1 = 2^1*2^1*3^1*82^1
986 = 17^1*58^1
987 = 3^1*7^1*47^1
992 = 4^1*248^1 = 2^1*2^1*4^1*62^1 = 2^1*2^1*8^1*31^1 = 2^1*2^1*2^1*2^1*2^1*31^1
998 = 2^1*499^1