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

0,3

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A000203, A051027, A139041.

Sequence in context: A075624 A008333 A076295 * A310779 A083030 A310780

Adjacent sequences: A280098 A280099 A280100 * A280102 A280103 A280104

Keyword

nonn

Author

Omar E. Pol, Dec 25 2016

Status

approved