A294236 - OEIS

A294236

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

0, 0, 0, 0, 1, 2, 3, 4, 1, 3, 5, 7, 10, 13, 16, 19, 14, 17, 11, 14, 18, 22, 26, 30, 22, 27, 32, 38, 45, 52, 59, 66, 57, 64, 71, 78, 67, 74, 81, 88, 75, 82, 89, 96, 104, 113, 122, 131, 116, 126, 111, 121, 132, 143, 127, 138, 121, 132, 143, 154, 166, 178, 190

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

OFFSET

1,6

LINKS

Table of n, a(n) for n=1..63.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A008683, A008966, A294237.