A272024 Number of partitions of the sum of the divisors of n.

1, 3, 5, 15, 11, 77, 22, 176, 101, 385, 77, 3718, 135, 1575, 1575, 6842, 385, 31185, 627, 53174, 8349, 17977, 1575, 966467, 6842, 53174, 37338, 526823, 5604, 5392783, 8349, 1505499, 147273, 386155, 147273, 64112359, 26015, 966467, 526823, 56634173, 53174, 118114304, 75175, 26543660, 12132164, 5392783

Offset: 1

Author

Omar E. Pol, Apr 19 2016

Keywords

• nonn

Comments

Also number of partitions of the total number of parts in the partitions of n into equal parts.

Note that one of the partitions of the sum of the divisors of n is also the list of divisors of n in decreasing order, see example.

Examples

			For n = 9 the sum of the divisors of 9 is 1 + 3 + 9 = 13 and the number of partitions of 13 is A000041(13) = 101, so a(9) = 101.
Note that one of the 101 partitions of 13 is [9, 3, 1] and it is also the list of divisors of 9 in decreasing order.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A000203, A056538, A058699, A072861, A139041, A272209.

Programs

Mathematica

Table[PartitionsP@ DivisorSigma[1, n], {n, 46}] (* Michael De Vlieger, Apr 19 2016 *)

PARI

a(n) = numbpart(sigma(n)); \\ Michel Marcus, Apr 19 2016

Formula

a(n) = p(sigma(n)) = A000041(A000203(n)).