A303051 Number of partitions of n into two distinct parts (p,q) such that p, q and p+q are all squarefree.

0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 0, 3, 2, 3, 0, 4, 0, 3, 0, 4, 4, 4, 0, 0, 4, 0, 0, 5, 4, 5, 0, 6, 6, 6, 0, 7, 6, 7, 0, 8, 7, 9, 0, 0, 7, 8, 0, 0, 0, 7, 0, 10, 0, 7, 0, 10, 10, 9, 0, 11, 10, 0, 0, 11, 10, 11, 0, 12, 12, 11, 0, 13, 13, 0, 0, 14, 12, 14, 0, 0

Offset: 1

Author

Wesley Ivan Hurt, Apr 17 2018

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A302986.

Programs

Mathematica

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

PARI

a(n) = sum(i=1, (n-1)\2, moebius(n)^2*moebius(i)^2*moebius(n-i)^2); \\ Michel Marcus, Apr 17 2018

Formula

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