Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Oct 25 2024 09:35:54
%S 1,6,12,64,24,256,48,512,60,96,2048,144,210,120,216,180,384,288,16384,
%T 240,432,420,65536,1536,360,480,900,864,3072,1152,1296,2310,524288,
%U 6144,960,720,840,2304,1728,1080,1260,2592,2097152,1800,4608,24576,4194304,1440,3456
%N Least value with A045779(n) factorizations into distinct factors.
%H David A. Corneth, <a href="/A045780/b045780.txt">Table of n, a(n) for n = 1..953</a>
%e From _Gus Wiseman_, Jan 11 2020: (Start)
%e The strict factorizations of a(n) for n = 1..9:
%e () (6) (12) (64) (24) (256) (48) (512) (60)
%e (2*3) (2*6) (2*32) (3*8) (4*64) (6*8) (8*64) (2*30)
%e (3*4) (4*16) (4*6) (8*32) (2*24) (16*32) (3*20)
%e (2*4*8) (2*12) (2*128) (3*16) (2*256) (4*15)
%e (2*3*4) (2*4*32) (4*12) (4*128) (5*12)
%e (2*8*16) (2*3*8) (2*4*64) (6*10)
%e (2*4*6) (2*8*32) (2*5*6)
%e (4*8*16) (3*4*5)
%e (2*3*10)
%e (End)
%e 30 is not in the sequence even though A045779(30) = 5. As 24 is the smallest k such that A045779(k) = 5 we have a(m) = 24 where m is such that A045779(m) = 5 which turns out to be m = 5 (not every positive integer is in A045779). So a(5) = 24. - _David A. Corneth_, Oct 24 2024
%Y All terms belong to A025487.
%Y The non-strict version is A045783.
%Y The sorted version is A330997.
%Y Factorizations are A001055 with image A045782 and complement A330976.
%Y Strict factorizations are A045778 with image A045779 and complement A330975.
%Y The least number with exactly n strict factorizations is A330974(n).
%Y Cf. A033833, A318286, A330972, A330973, A330989.
%K nonn
%O 1,2
%A _David W. Wilson_
%E More terms from _David A. Corneth_, Oct 24 2024