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A360568
Number of divisors d of n such that n - d is not square.
0
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved