cp's OEIS Frontend

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

%I A162329 #19 Mar 11 2019 11:58:50
%S A162329 0,1,5,13,29,54,97,161,257,402,604,896,1299,1866,2616,3665,5031,6891,
%T A162329 9290,12498,16600,22008,28841,37740,48919,63294,81230,104048,132355,
%U A162329 168048,212070,267105,334671,418486,520857,647081,800531,988510,1216159,1493430
%N A162329 Sum of all parts of the partitions of n, minus sigma(n).
%C A162329 Apart from the offset the same as A086732.
%C A162329 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
%F A162329 a(n) = A066186(n) - A000203(n).
%e A162329 a(1) =  1 -  1 =  0;
%e A162329 a(2) =  4 -  3 =  1;
%e A162329 a(3) =  9 -  4 =  5;
%e A162329 a(6) = 66 - 12 = 54.
%p A162329 A066186 := proc(n) n*combinat[numbpart](n) ; end:
%p A162329 A000203 := proc(n) numtheory[sigma](n) ; end:
%p A162329 A162329 := proc(n) A066186(n)-A000203(n) ; end: seq(A162329(n),n=1..80) ; # _R. J. Mathar_, Aug 14 2009
%t A162329 Table[Total[Flatten[IntegerPartitions[n]]]-DivisorSigma[1,n],{n,40}] (* _Harvey P. Dale_, Mar 21 2013 *)
%o A162329 (PARI) a(n) = n*numbpart(n) - sigma(n); \\ _Michel Marcus_, Mar 10 2019
%Y A162329 Cf. A000203, A066186, A086732, A161975.
%K A162329 nonn
%O A162329 1,3
%A A162329 _Juri-Stepan Gerasimov_, Jul 01 2009
%E A162329 a(6), a(8), a(24) corrected by _R. J. Mathar_, Aug 14 2009