The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103277 Smallest i such that there exists j such that i = x + y + z, j = x*y*z has exactly n solutions in positive integers x <= y <= z. 7
3, 13, 39, 118, 185, 400, 511, 1022, 1287, 2574, 4279, 8558, 11777, 24377, 23554, 46111, 99085, 165490 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Least number k such that there exists n partitions of k into 3 parts each having the same product.
The greatest number k such that there exists n partitions of k into 3 parts each having the same product: 18, 102, 492, 1752, ...
The number of members in each "class" of the set having n partitions into 3 parts each having the same product: 12, 54, 147, 397, ....
LINKS
EXAMPLE
3 = 1+1+1 & 1*1*1 = 1.
13 = 6+6+1 = 9+2+2 & 6*6*1 = 9*2*2 = 36.
39 = 20+15+4 = 24+10+5 = 25+8+6 & 20*15*4 = 24*10*5 = 25*8*6 = 1200.
118 = 54+50+14 = 63+40+15 = 70+30+18 = 72+25+21 & 54*50*14 = 63*40*15 = 70*30*18 = 72*25*21 = 37800.
185 = 90+84+11 = 110+63+12 = 126+44+15 = 132+35+18 = 135+28+22 & 90*84*11 = 110*63*12 = 126*44*15 = 132*35*18 = 135*28*22 = 83160.
400 = 196+180+24 = 245+128+27 = 252+120+28 = 270+98+32 = 280+84+36 = 288+70+42 & 196*180*24 = 245*128*27 = 252*120*28 = 270*98*32 = 280*84*36 = 288*70*42 = 846720.
511 = 260+216+35 = 280+195+36 = 315+156+40 = 325+144+42 = 336+130+45 = 360+91+60 = 364+75+72 & 260*216*35 = 280*195*36 = 315*156*40 = 325*144*42 = 336*130*45 = 360*91*60 = 364*75*72 = 1965600.
1022 = 520+432+70 = 560+390+72 = 630+312+80 = 650+288+84 = 672+260+90 = 675+256+91 = 720+182+120 = 728+150+144 & 520*432*70 = 560*390*72 = 630*312*80 = 650*288*84 = 672*260*90 = 675*256*91 = 720*182*120 = 728*150*144 = 15724800.
1287 = 600+588+99 = 648+539+100 = 720+462+105 = 770+405+112 = 825+336+126 = 840+315+132 = 880+245+162 = 882+240+165 = 891+200+196 & 600*588*99 = 648*539*100 = 720*462*105 = 770*405*112 = 825*336*126 = 840*315*132 = 880*245*162 = 882*240*165 = 891*200*196 = 34927200.
From Donovan Johnson, Mar 29 2010: (Start)
2574 = 198+1176+1200 = 200+1078+1296 = 210+924+1440 = 224+810+1540 = 231+768+1575 = 252+672+1650 = 264+630+1680 = 324+490+1760 = 330+480+1764 = 392+400+1782 & 198*1176*1200 = 200*1078*1296 = 210*924*1440 = 224*810*1540 = 231*768*1575 = 252*672*1650 = 264*630*1680 = 324*490*1760 = 330*480*1764 = 392*400*1782 = 279417600.
4279 = 378+1925+1976 = 380+1820+2079 = 385+1710+2184 = 399+1540+2340 = 429+1330+2520 = 440+1274+2565 = 504+1045+2730 = 532+975+2772 = 550+936+2793 = 637+792+2850 = 684+735+2860 & 378*1925*1976 = 380*1820*2079 = 385*1710*2184 = 399*1540*2340 = 429*1330*2520 = 440*1274*2565 = 504*1045*2730 = 532*975*2772 = 550*936*2793 = 637*792*2850 = 684*735*2860 = 1437836400.
8558 = 756+3850+3952 = 760+3640+4158 = 770+3420+4368 = 798+3080+4680 = 858+2660+5040 = 880+2548+5130 = 896+2475+5187 = 1008+2090+5460 = 1064+1950+5544 = 1100+1872+5586 = 1274+1584+5700 = 1368+1470+5720 & 756*3850*3952 = 760*3640*4158 = 770*3420*4368 = 798*3080*4680 = 858*2660*5040 = 880*2548*5130 = 896*2475*5187 = 1008*2090*5460 = 1064*1950*5544 = 1100*1872*5586 = 1274*1584*5700 = 1368*1470*5720 = 11502691200.
11777 = 171+5600+6006 = 175+4914+6688 = 198+3675+7904 = 224+3003+8550 = 228+2925+8624 = 240+2717+8820 = 245+2640+8892 = 385+1512+9880 = 416+1386+9975 = 462+1235+10080 = 540+1045+10192 = 600+936+10241 = 637+880+10260 & 171*5600*6006 = 175*4914*6688 = 198*3675*7904 = 224*3003*8550 = 228*2925*8624 = 240*2717*8820 = 245*2640*8892 = 385*1512*9880 = 416*1386*9975 = 462*1235*10080 = 540*1045*10192 = 600*936*10241 = 637*880*10260 = 5751345600.
24377 = 1196+11400+11781 = 1197+11220+11960 = 1232+9690+13455 = 1254+9200+13923 = 1360+7722+15295 = 1520+6435+16422 = 1547+6270+16560 = 1748+5304+17325 = 1890+4807+17680 = 1932+4680+17765 = 2244+3933+18200 = 2261+3900+18216 = 2448+3575+18354 = 2907+2990+18480 & 1196*11400*11781 = 1197*11220*11960 = 1232*9690*13455 = 1254*9200*13923 = 1360*7722*15295 = 1520*6435*16422 = 1547*6270*16560 = 1748*5304*17325 = 1890*4807*17680 = 1932*4680*17765 = 2244*3933*18200 = 2261*3900*18216 = 2448*3575*18354 = 2907*2990*18480 = 160626866400.
23554 = 342+11200+12012 = 350+9828+13376 = 351+9728+13475 = 396+7350+15808 = 448+6006+17100 = 456+5850+17248 = 480+5434+17640 = 490+5280+17784 = 665+3584+19305 = 770+3024+19760 = 832+2772+19950 = 924+2470+20160 = 1080+2090+20384 = 1200+1872+20482 = 1274+1760+20520 & 342*11200*12012 = 350*9828*13376 = 351*9728*13475 = 396*7350*15808 = 448*6006*17100 = 456*5850*17248 = 480*5434*17640 = 490*5280*17784 = 665*3584*19305 = 770*3024*19760 = 832*2772*19950 = 924*2470*20160 = 1080*2090*20384 = 1200*1872*20482 = 1274*1760*20520 = 46010764800.
(End)
From Duncan Moore, Sep 02 2017: (Start)
46111 = 4446+20160+21505 = 4455+19760+21896 = 4576+17595+23940 = 4680+16560+24871 = 4725+16192+25194 = 4807+15600+25704 = 4928+14858+26325 = 5100+13984+27027 = 5187+13600+27324 = 5520+12376+28215 = 5610+12096+28405 = 5712+11799+28600 = 6270+10465+29376 = 7360+8721+30030 = 7735+8280+30096 = 7904+8100+30107 & 4446*20160*21505 = 4455*19760*21896 = 4576*17595*23940 = 4680*16560*24871 = 4725*16192*25194 = 4807*15600*25704 = 4928*14858*26325 = 5100*13984*27027 = 5187*13600*27324 = 5520*12376*28215 = 5610*12096*28405 = 5712*11799*28600 = 6270*10465*29376 = 7360*8721*30030 = 7735*8280*30096 = 7904*8100*30107 = 1927522396800.
99085 = 3770+47120+48195 = 3780+45240+50065 = 3952+37758+57375 = 3978+37107+58000 = 4176+33250+61659 = 4199+32886+62000 = 4216+32625+62244 = 4495+29070+65520 = 4500+29016+65569 = 4914+25296+68875 = 5320+22620+71145 = 7280+15390+76415 = 7395+15120+76570 = 7905+14040+77140 = 8370+13195+77520 = 9367+11718+78000 = 9945+11020+78120 & 3770*47120*48195 = 3780*45240*50065 = 3952*37758*57375 = 3978*37107*58000 = 4176*33250*61659 = 4199*32886*62000 = 4216*32625*62244 = 4495*29070*65520 = 4500*29016*65569 = 4914*25296*68875 = 5320*22620*71145 = 7280*15390*76415 = 7395*15120*76570 = 7905*14040*77140 = 8370*13195*77520 = 9367*11718*78000 = 9945*11020*78120 = 8561475468000.
165490 = 14000+72488+79002 = 14022+71500+79968 = 14080+69615+81795 = 14280+65520+85690 = 14432+63308+87750 = 14820+59040+91630 = 14896+58344+92250 = 16236+49504+99750 = 16380+48790+100320 = 16830+46740+101920 = 17290+44880+103320 = 17589+43776+104125 = 18720+40180+106590 = 19152+39000+107338 = 20090+36720+108680 = 21648+33592+110250 = 23940+30030+111520 = 25840+27720+111930 & 14000*72488*79002 = 14022*71500*79968 = 14080*69615*81795 = 14280*65520*85690 = 14432*63308*87750 = 14820*59040*91630 = 14896*58344*92250 = 16236*49504*99750 = 16380*48790*100320 = 16830*46740*101920 = 17290*44880*103320 = 17589*43776*104125 = 18720*40180*106590 = 19152*39000*107338 = 20090*36720*108680 = 21648*33592*110250 = 23940*30030*111520 = 25840*27720*111930 = 80173757664000
(End)
MATHEMATICA
tanya[n_] := tanya[n] = Max[Length /@ Split[ Sort[Times @@@ Partition[Last /@ Flatten[ FindInstance[a + b + c == n && a >= b >= c > 0, {a, b, c}, Integers, Round[n^2/12]]], 3]]]];
CROSSREFS
See A103278 for least j associated with i = A103277(n).
Sequence in context: A103657 A320661 A122504 * A166897 A167910 A147042
KEYWORD
nonn,more
AUTHOR
David W. Wilson, Jan 27 2005
EXTENSIONS
Additional comments and examples from Joseph Biberstine (jrbibers(AT)indiana.edu) and Robert G. Wilson v, Jul 27 2006
Edited by N. J. A. Sloane, Apr 29 2007
a(10)-a(15) from Donovan Johnson, Mar 29 2010
a(16)-a(18) from Duncan Moore, Sep 02 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 16:46 EDT 2024. Contains 373432 sequences. (Running on oeis4.)