A389780 Number of divisors d of n such that gcd(d^2 - 1, n) = 1 and gcd((n/d)^2 - 1, n) != 1.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 3, 1, 2, 2, 3, 1, 1, 1, 2, 1, 2, 1, 4, 1, 3, 2, 2, 1, 3, 2, 1, 2, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 2, 3, 1, 4, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 5

Offset

1,10

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Mathematica

a[n_]:=Length[Select[Divisors[n], GCD[#^2-1, n]==1&&GCD[(n/#)^2-1, n]!=1&]]; Array[a, 96] (* James C. McMahon, Oct 27 2025 *)

Prog

(Magma) [#[d: d in Divisors(n) | Gcd(d^2 - 1, n) eq 1 and not Gcd((n div d)^2 - 1, n) eq 1]: n in [1..96]];

Crossrefs

Cf. A000005, A000010, A386476.

Sequence in context: A023582 A306717 A195969 * A023518 A326194 A331251

Adjacent sequences: A389777 A389778 A389779 * A389781 A389782 A389783

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 14 2025

Status

approved