A351833 Number of partitions of n into exactly two parts, at least one of which is squarefree.

0, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 7, 7, 6, 7, 8, 9, 8, 9, 10, 11, 9, 11, 12, 12, 11, 12, 14, 14, 12, 14, 15, 16, 12, 16, 18, 18, 15, 18, 20, 19, 17, 19, 22, 22, 18, 21, 23, 24, 19, 22, 23, 26, 21, 24, 25, 27, 23, 26, 28, 28, 24, 28, 30, 30, 25, 30, 31, 33, 24, 32, 33, 34, 28

Offset

1,4

Links

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

Formula

a(n) = Sum_{k=1..floor(n/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), A351834 (two distinct parts).

Sequence in context: A005350 A055037 A227386 * A354967 A125186 A226222

Adjacent sequences: A351830 A351831 A351832 * A351834 A351835 A351836

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 21 2022

Status

approved