A351834 Number of partitions of n into exactly two distinct parts, at least one of which is squarefree.

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 7, 9, 9, 11, 9, 11, 11, 12, 10, 12, 13, 14, 12, 14, 14, 16, 12, 16, 17, 18, 15, 18, 19, 19, 16, 19, 21, 22, 18, 21, 23, 24, 18, 22, 23, 26, 21, 24, 24, 27, 22, 26, 27, 28, 24, 28, 29, 30, 24, 30, 30, 33, 24, 32, 32, 34, 27

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Formula

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

Crossrefs

Cf. A005117, A008683 (mu), A351833.

Sequence in context: A167232 A319468 A137791 * A096125 A140828 A262907

Adjacent sequences: A351831 A351832 A351833 * A351835 A351836 A351837

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 21 2022

Status

approved