A294244 - OEIS

A294244

Sum of the smaller parts of the partitions of 2n into two parts with larger part nonsquarefree.

0, 0, 2, 4, 3, 7, 13, 19, 17, 14, 22, 30, 27, 38, 52, 66, 64, 78, 74, 88, 82, 96, 113, 131, 126, 121, 143, 138, 132, 154, 178, 203, 197, 223, 251, 279, 271, 300, 332, 364, 357, 391, 427, 463, 455, 446, 484, 522, 512, 502, 492, 532, 520, 560, 546, 586, 570

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..n} i * (1 - mu(2*n-i)^2), where mu is the Möbius function (A008683).

MATHEMATICA

Table[Sum[k (1 - MoebiusMu[2 n - k]^2), {k, n}], {n, 80}]

PROG

(PARI) a(n) = sum(i=1, n, i*(1 - moebius(2*n-i)^2)); \\ Michel Marcus, Feb 11 2018