A389362 - OEIS

A389362

Number of divisors d of n such that d^2 - 1 is not relatively prime to n.

0, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 4, 1, 2, 2, 1, 1, 4, 1, 3, 2, 2, 1, 5, 1, 2, 1, 2, 1, 7, 1, 1, 2, 2, 1, 5, 1, 2, 2, 3, 1, 7, 1, 2, 3, 2, 1, 6, 1, 3, 2, 2, 1, 5, 2, 3, 2, 2, 1, 9, 1, 2, 2, 1, 1, 6, 1, 2, 2, 5, 1, 6, 1, 2, 3, 2, 1, 6, 1, 4, 1, 2, 1, 9, 1, 2, 2, 2, 1, 9

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OFFSET

1,6

COMMENTS

a(n) >= 1 for n >= 2, as for d = 1 we have gcd(0,n) = n. a(n) = 1 if n is in A246655, or if n = p*q with p < q prime and q not == +- 1 (mod p). - Robert Israel, Oct 01 2025

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000005(n) - A386476(n).

MAPLE

f:= proc(n) nops(select(t -> igcd(t^2-1, n)<>1, numtheory:-divisors(n))) end proc:map(f, [$1..100]); # Robert Israel, Oct 01 2025

MATHEMATICA

A389362[n_] := DivisorSum[n, 1 &, !CoprimeQ[#^2 - 1, n] &];

Array[A389362, 100] (* Paolo Xausa, Oct 14 2025 *)

PROG

(Magma) [#[d: d in Divisors(n) | not Gcd(d^2 - 1, n) eq 1]: n in [1..90]];

(PARI) a(n) = sumdiv(n, d, gcd(d^2-1, n) != 1); \\ Michel Marcus, Oct 01 2025