A334671 Number of ways to write n as the sum of a squarefree number (A005117) and a square (A000290).

1, 2, 2, 1, 2, 3, 3, 1, 1, 3, 4, 2, 1, 4, 4, 2, 3, 3, 4, 2, 3, 4, 5, 2, 1, 5, 4, 2, 2, 6, 5, 3, 3, 3, 6, 2, 4, 7, 7, 3, 3, 7, 5, 3, 2, 6, 7, 3, 2, 5, 7, 3, 3, 4, 7, 4, 4, 5, 7, 4, 2, 8, 5, 3, 4, 8, 7, 4, 5, 7, 9, 3, 4, 7, 7, 2, 5, 9, 6, 4, 3, 8, 10, 4, 3, 9, 10, 4, 4, 6

Offset: 1

Author

Michel Marcus, Oct 31 2020

Keywords

• nonn

Comments

Differs from A085263 where the square cannot be zero.

Links

• Jorge Urroz, Every integer can be written as a square plus a squarefree, arXiv:2010.15580 [math.NT], 2020.

Crossrefs

Cf. A000290, A005117, A085263 (with a positive square).

Programs

PARI

a(n) = sum(k=0, n, issquare(k) * issquarefree(n-k));