A280101 a(n) = sigma(sigma(p(n))) = sum of the divisors of the sum of the divisors of number of partitions of n.

1, 1, 4, 7, 12, 15, 28, 60, 91, 195, 252, 360, 252, 216, 744, 896, 1020, 1512, 1651, 2400, 3048, 7644, 6552, 4800, 6720, 10890, 24384, 19812, 17360, 20160, 45136, 35280, 40320, 54600, 78624, 68400, 27540, 79248, 115200, 219583, 265980, 200312, 268800, 335160

Offset: 0

Author

Omar E. Pol, Dec 25 2016

Keywords

• nonn

Examples

			For n = 7 the number of partitions of 7 is p(7) = 15, and the sum of the divisors of 15 is sigma(15) = 1 + 3 + 5 + 15 = 24, and the sum of the divisors of 24 is sigma(24) = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60, so a(7) = 60.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A000041, A000203, A051027, A139041.

Programs

Mathematica

Array[DivisorSigma[1, DivisorSigma[1, PartitionsP[#]]]&, 43, 0] (* Amiram Eldar, Feb 19 2019 *)

PARI

a(n) = sigma(sigma(numbpart(n))); \\ Michel Marcus, Feb 19 2019

Formula

a(n) = A000203(A000203(A000041(n))) = A051027(A000041(n)).

a(n) = A000203(A139041(n)), n >= 1.