A162329 Sum of all parts of the partitions of n, minus sigma(n).

0, 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, 1493430

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 01 2009

Keywords

• nonn

Comments

Apart from the offset the same as A086732.

Sum of all parts of all partitions of n minus the total number of parts in the partitions of n into equal parts. - Omar E. Pol, Jan 24 2014

Examples

			a(1) =  1 -  1 =  0;
a(2) =  4 -  3 =  1;
a(3) =  9 -  4 =  5;
a(6) = 66 - 12 = 54.
		

Crossrefs

Cf. A000203, A066186, A086732, A161975.

Programs

Maple

A066186 := proc(n) n*combinat[numbpart](n) ; end:
A000203 := proc(n) numtheory[sigma](n) ; end:
A162329 := proc(n) A066186(n)-A000203(n) ; end: seq(A162329(n),n=1..80) ; # R. J. Mathar, Aug 14 2009

Mathematica

Table[Total[Flatten[IntegerPartitions[n]]]-DivisorSigma[1,n],{n,40}] (* Harvey P. Dale, Mar 21 2013 *)

PARI

a(n) = n*numbpart(n) - sigma(n); \\ Michel Marcus, Mar 10 2019

Formula

a(n) = A066186(n) - A000203(n).

Extensions

a(6), a(8), a(24) corrected by R. J. Mathar, Aug 14 2009