A303165 Sum of the squarefree differences |q-p| of the parts in the partitions of n into two distinct parts (p,q) where p < q.

0, 0, 1, 2, 4, 2, 9, 8, 16, 8, 16, 18, 27, 18, 40, 32, 55, 32, 72, 32, 91, 32, 112, 54, 135, 54, 135, 80, 135, 80, 164, 110, 195, 110, 228, 144, 263, 144, 300, 182, 339, 182, 380, 224, 423, 224, 423, 270, 470, 270, 470, 270, 521, 270, 574, 270, 629, 270, 686

Offset

1,4

Links

Table of n, a(n) for n=1..59.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Sum[(n - 2 i) MoebiusMu[n - 2 i]^2, {i, Floor[(n - 1)/2]}], {n, 100}]

Crossrefs

Cf. A008683, A303205.

Sequence in context: A058942 A365638 A196759 * A188813 A324958 A353108

Adjacent sequences: A303162 A303163 A303164 * A303166 A303167 A303168

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 19 2018

Status

approved