A294242 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..71.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

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

PROG

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