login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Least value with A045779(n) factorizations into distinct factors.
16

%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