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

1,7

Links

Table of n, a(n) for n=1..81.

Index entries for sequences related to partitions

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A008683, A302986.

Sequence in context: A357237 A277808 A105964 * A324044 A364046 A001899

Adjacent sequences: A303048 A303049 A303050 * A303052 A303053 A303054

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 17 2018

Status

approved