A294245 Sum of the larger parts of the partitions of 2n into two parts with larger part nonsquarefree.

0, 0, 4, 4, 17, 17, 29, 29, 37, 46, 66, 66, 103, 130, 158, 158, 174, 174, 192, 192, 212, 212, 301, 301, 374, 399, 451, 478, 506, 506, 566, 629, 661, 661, 729, 729, 765, 840, 916, 916, 1037, 1037, 1121, 1121, 1165, 1210, 1302, 1302, 1350, 1498, 1548, 1548

Offset: 1

Author

Wesley Ivan Hurt, Oct 25 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A008966, A294246.

Programs

Mathematica

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

PARI

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

Formula

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