A294103 Sum of the differences of the larger and smaller parts in the partitions of 2n into two squarefree parts or two nonsquarefree parts.

0, 2, 4, 12, 4, 24, 20, 54, 40, 72, 70, 114, 62, 116, 62, 182, 126, 292, 134, 330, 182, 412, 190, 460, 202, 468, 380, 518, 490, 632, 462, 692, 458, 890, 562, 1184, 638, 1088, 590, 1206, 590, 1430, 678, 1556, 986, 1578, 952, 1772, 1032, 1876, 1214, 1986, 1326

Offset: 1

Author

Wesley Ivan Hurt, Oct 22 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008966, A294097.

Programs

Mathematica

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

Formula

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