%I #5 Jul 21 2022 07:40:35
%S 1,1,1,1,1,2,2,2,2,4,4,8,8,16,32,32,32,64,64,128,256,512,512,1024,
%T 1024,2048,2048,4096,4096,12288,12288,12288,24576,49152,98304,196608,
%U 196608,393216,786432,1572864,1572864,4718592,4718592,9437184,18874368,37748736
%N Number of ways to choose a sequence of prime factors, one of each integer from 2 to n.
%C Also partial products of A001221 without the first term 0, sum A013939.
%C For initial terms up to n = 29 we have a(n) = 2^A355538(n). The first non-power of 2 is a(30) = 12288.
%e The a(n) choices for n = 2, 6, 10, 12, with prime(k) replaced by k:
%e (1) (12131) (121314121) (12131412151)
%e (12132) (121314123) (12131412152)
%e (121324121) (12131412351)
%e (121324123) (12131412352)
%e (12132412151)
%e (12132412152)
%e (12132412351)
%e (12132412352)
%t Table[Times@@PrimeNu/@Range[2,m],{m,2,30}]
%Y The sum of the same integers is A000096.
%Y The product of the same integers is A000142, Heinz number A070826.
%Y The version for divisors instead of prime factors is A066843.
%Y The integers themselves are the rows of A131818.
%Y The version with multiplicity is A327486.
%Y Using prime indices instead of 2..n gives A355741, for multisets A355744.
%Y Counting sequences instead of multisets gives A355746.
%Y A001221 counts distinct prime factors, with sum A001414.
%Y A001222 counts prime factors with multiplicity.
%Y A003963 multiplies together the prime indices of n.
%Y A056239 adds up prime indices, row sums of A112798.
%Y Cf. A000005, A000040, A000720, A002110, A013939, A076610, A355538, A355731, A355733, A355745, A355747.
%K nonn
%O 1,6
%A _Gus Wiseman_, Jul 20 2022