A360568 Number of divisors d of n such that n - d is not square.

0, 0, 1, 2, 0, 2, 1, 2, 2, 2, 1, 4, 1, 3, 3, 4, 0, 3, 1, 4, 3, 3, 1, 6, 2, 2, 3, 5, 1, 6, 1, 4, 3, 3, 3, 8, 0, 2, 2, 6, 1, 6, 1, 5, 4, 3, 1, 8, 2, 3, 3, 5, 1, 6, 3, 6, 3, 3, 1, 11, 1, 3, 5, 6, 2, 6, 1, 4, 3, 7, 1, 9, 1, 3, 5, 5, 3, 7, 1, 8, 4, 2, 1, 10, 3, 3, 3, 7, 1, 10, 3, 5, 3, 3, 3, 10, 1, 4, 5, 8

Offset

1,4

Links

Table of n, a(n) for n=1..100.

Index entries for sequences related to divisors

Example

a(4) = 2 because 4 has divisors 1, 2, and 4, and 4 - 1 = 3 and 4 - 2 = 2 are not squares.

Mathematica

a[n_] := DivisorSum[n, 1 &, ! IntegerQ[Sqrt[n - #]] &]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)

Prog

(Magma) [#[d: d in Divisors(n) | not IsSquare(n-d)]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, !issquare(n-d)); \\ Michel Marcus, Feb 12 2023

Crossrefs

Cf. A000037, A027750, A360017.

Sequence in context: A141454 A301564 A334361 * A219791 A029345 A153149

Adjacent sequences: A360565 A360566 A360567 * A360569 A360570 A360571

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 12 2023

Status

approved