A272209 Number of partitions of the number of divisors of n.

1, 2, 2, 3, 2, 5, 2, 5, 3, 5, 2, 11, 2, 5, 5, 7, 2, 11, 2, 11, 5, 5, 2, 22, 3, 5, 5, 11, 2, 22, 2, 11, 5, 5, 5, 30, 2, 5, 5, 22, 2, 22, 2, 11, 11, 5, 2, 42, 3, 11, 5, 11, 2, 22, 5, 22, 5, 5, 2, 77, 2, 5, 11, 15, 5, 22, 2, 11, 5, 22, 2, 77, 2, 5, 11, 11, 5, 22, 2, 42, 7, 5, 2, 77

Offset: 1

Author

Omar E. Pol, Apr 25 2016

Keywords

• nonn

Examples

			For n = 12 the divisors of 12 are 1, 2, 3, 4, 6, 12. There are 6 divisors of 12 and the number of partitions of 6 is A000041(6) = 11, so a(12) = 11.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000041, A035116, A058699, A085543, A272024.

Programs

Mathematica

Table[PartitionsP@ DivisorSigma[0, n], {n, 120}] (* Michael De Vlieger, Apr 25 2016 *)

PARI

a(n) = numbpart(numdiv(n)); \\ Michel Marcus, Apr 26 2016

Formula

a(n) = p(d(n)) = A000041(A000005(n)).