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%I #21 Feb 26 2023 03:32:37
%S 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,
%T 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,
%U 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
%N Number of divisors d of n such that n - d is not square.
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%e a(4) = 2 because 4 has divisors 1, 2, and 4, and 4 - 1 = 3 and 4 - 2 = 2 are not squares.
%t a[n_] := DivisorSum[n, 1 &, ! IntegerQ[Sqrt[n - #]] &]; Array[a, 100] (* _Amiram Eldar_, Feb 12 2023 *)
%o (Magma) [#[d: d in Divisors(n) | not IsSquare(n-d)]: n in [1..100]];
%o (PARI) a(n) = sumdiv(n, d, !issquare(n-d)); \\ _Michel Marcus_, Feb 12 2023
%Y Cf. A000037, A027750, A360017.
%K nonn
%O 1,4
%A _Juri-Stepan Gerasimov_, Feb 12 2023