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

1,2

Comments

Differs from A085263 where the square cannot be zero.

Links

Table of n, a(n) for n=1..90.

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

Prog

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

Crossrefs

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

Sequence in context: A351524 A054711 A241424 * A294232 A331254 A193738

Adjacent sequences: A334668 A334669 A334670 * A334672 A334673 A334674

Keyword

nonn

Author

Michel Marcus, Oct 31 2020

Status

approved