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A334671 Number of ways to write n as the sum of a squarefree number (A005117) and a square (A000290). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A070680 A054711 A241424 * A294232 A331254 A193738

Adjacent sequences:  A334668 A334669 A334670 * A334672 A334673 A334674

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 31 2020

STATUS

approved

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Last modified October 18 03:25 EDT 2021. Contains 348065 sequences. (Running on oeis4.)