A294244 Sum of the smaller parts of the partitions of 2n into two parts with larger part nonsquarefree.

0, 0, 2, 4, 3, 7, 13, 19, 17, 14, 22, 30, 27, 38, 52, 66, 64, 78, 74, 88, 82, 96, 113, 131, 126, 121, 143, 138, 132, 154, 178, 203, 197, 223, 251, 279, 271, 300, 332, 364, 357, 391, 427, 463, 455, 446, 484, 522, 512, 502, 492, 532, 520, 560, 546, 586, 570

Offset

1,3

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Prog

(PARI) a(n) = sum(i=1, n, i*(1 - moebius(2*n-i)^2)); \\ Michel Marcus, Feb 11 2018

Crossrefs

Cf. A008683, A008966, A294243.

Sequence in context: A035507 A138612 A246680 * A333028 A296449 A309201

Adjacent sequences: A294241 A294242 A294243 * A294245 A294246 A294247

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 25 2017

Status

approved