A294211 Sum of the parts in the partitions of n into two squarefree parts or two nonsquarefree parts.

0, 2, 3, 8, 5, 12, 14, 32, 18, 20, 22, 60, 52, 42, 45, 112, 85, 90, 57, 160, 105, 132, 92, 240, 150, 156, 162, 280, 203, 180, 186, 384, 264, 306, 245, 612, 333, 304, 312, 640, 410, 378, 473, 792, 585, 414, 423, 912, 637, 500, 408, 1092, 742, 756, 440, 1120

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Crossrefs

Cf. A008966, A294209, A294210.

Sequence in context: A328846 A249154 A262351 * A097505 A343072 A352844

Adjacent sequences: A294208 A294209 A294210 * A294212 A294213 A294214

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 24 2017

Status

approved