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A294239

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

0, 0, 0, 0, 5, 6, 7, 8, 9, 20, 22, 24, 39, 42, 45, 48, 51, 54, 57, 60, 84, 88, 92, 96, 100, 130, 135, 168, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 360, 414, 423, 432, 441, 500, 510, 520, 583, 594, 605, 616, 627, 638

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

OFFSET

1,5

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

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

PROG

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