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

1,3

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

Links

Table of n, a(n) for n=1..40.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A066186, A086732, A161975.

Sequence in context: A240130 A005473 A086732 * A299895 A307674 A273026

Adjacent sequences: A162326 A162327 A162328 * A162330 A162331 A162332

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 01 2009

Extensions

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

Status

approved