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

Author

Jon Perry, Jul 29 2003

Keywords

• nonn

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

Crossrefs

Cf. A000041, A066186, A000203, A162329.

Programs

Magma

[ (n+1)*NumberOfPartitions(n+1)-SumOfDivisors(n+1): n in [1..38] ]; // Klaus Brockhaus, Jul 07 2009

Mathematica

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

PARI

a(n) = (n+1)*numbpart(n+1) - sigma(n+1); \\ Michel Marcus, Feb 19 2018

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

Extensions

More terms from Klaus Brockhaus, Jul 07 2009

Definition clarified by Omar E. Pol, Feb 13 2021