A086732 Convolution of A000203 with partition function (A000041) of positive integers.

1, 5, 13, 29, 54, 97, 161, 257, 402, 604, 896, 1299, 1866, 2616, 3665, 5031, 6891, 9290, 12498, 16600, 22008, 28841, 37740, 48919, 63294, 81230, 104048, 132355, 168048, 212070, 267105, 334671, 418486, 520857, 647081, 800531, 988510, 1216159

Offset

1,2

Comments

Another version of the convolution of A000203 but starting from A000041(0) = 1 is given by the nonzero terms of A066186. - Omar E. Pol, Feb 13 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = (n+1)*A000041(n+1) - A000203(n+1). - Vladeta Jovovic, Apr 08 2006

a(n) = A066186(n+1) - A000203(n+1). - Omar E. Pol, Feb 13 2021

Mathematica

Table[n PartitionsP[n]-DivisorSigma[1, n], {n, 2, 40}] (* Harvey P. Dale, Jun 28 2012 *)

Prog

(Magma) [ (n+1)*NumberOfPartitions(n+1)-SumOfDivisors(n+1): n in [1..38] ]; // Klaus Brockhaus, Jul 07 2009
(PARI) a(n) = (n+1)*numbpart(n+1) - sigma(n+1); \\ Michel Marcus, Feb 19 2018

Crossrefs

Cf. A000041, A066186, A000203, A162329.

Sequence in context: A350687 A240130 A005473 * A162329 A299895 A307674

Adjacent sequences: A086729 A086730 A086731 * A086733 A086734 A086735

Keyword

nonn

Author

Jon Perry, Jul 29 2003

Extensions

More terms from Klaus Brockhaus, Jul 07 2009

Definition clarified by Omar E. Pol, Feb 13 2021

Status

approved