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
Keywords
Examples
a(1) = 1 - 1 = 0; a(2) = 4 - 3 = 1; a(3) = 9 - 4 = 5; a(6) = 66 - 12 = 54.
Programs
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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
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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
Extensions
a(6), a(8), a(24) corrected by R. J. Mathar, Aug 14 2009
Comments