A168014 Sum of all parts of all partitions of n into equal parts that do not contain 1 as a part.

0, 0, 2, 3, 8, 5, 18, 7, 24, 18, 30, 11, 60, 13, 42, 45, 64, 17, 90, 19, 100, 63, 66, 23, 168, 50, 78, 81, 140, 29, 210, 31, 160, 99, 102, 105, 288, 37, 114, 117, 280, 41, 294, 43, 220, 225, 138, 47, 432, 98, 250, 153, 260, 53, 378

Offset: 0

Author

Omar E. Pol, Nov 20 2009

Keywords

• easy
• nonn

Comments

Sum of all the parts in the partitions of n into two parts such that the smaller part divides the larger. - Wesley Ivan Hurt, Dec 22 2017

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000005, A000041, A032741, A168015, A168020, A168021.

Programs

Maple

A168014:=n->n*(numtheory[tau](n)-1); seq(A168014(k), k=0..60); # Wesley Ivan Hurt, Oct 11 2013

Mathematica

Table[n*(DivisorSigma[0, n] - 1), {n, 0, 100}] (* Wesley Ivan Hurt, Oct 11 2013 *)

Formula

a(n) = n * A032741(n).

a(n) = n(d(n) - 1) = n*(A000005(n) - 1) = A038040(n) - n, if n >= 1. - Omar E. Pol, Jan 18 2013

Extensions

a(14)-a(55) from Vincenzo Librandi, May 25 2010

New name from Omar E. Pol, Jan 18 2013