A294209 Sum of the smaller parts in the partitions of n into two squarefree parts or two nonsquarefree parts.

0, 1, 1, 3, 2, 4, 3, 10, 5, 8, 6, 18, 15, 11, 8, 29, 26, 25, 13, 44, 34, 31, 19, 63, 41, 47, 44, 82, 53, 59, 36, 101, 64, 90, 49, 160, 79, 85, 66, 155, 98, 98, 123, 190, 156, 112, 107, 226, 147, 149, 126, 312, 175, 188, 142, 301, 202, 190, 173, 344, 232, 203

Offset

1,4

Links

Table of n, a(n) for n=1..62.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} i * [A008966(i) = A008966(n-i)], where [] is the Iverson bracket.

Mathematica

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

Crossrefs

Cf. A008966, A294210.

Sequence in context: A325705 A243407 A061721 * A066257 A085591 A062964

Adjacent sequences: A294206 A294207 A294208 * A294210 A294211 A294212

Keyword

easy,nonn

Author

Wesley Ivan Hurt, Oct 24 2017

Status

approved