A294242 Number of partitions of 2n into two parts with the larger part nonsquarefree.

0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 10, 10, 11, 11, 11, 11, 12, 13, 13, 13, 14, 14, 14, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 22, 22, 23, 23, 25, 25, 25, 25, 26, 27, 27, 27, 28

Offset: 1

Author

Wesley Ivan Hurt, Oct 25 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A008966, A057627.

Programs

Mathematica

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

PARI

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

Formula

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