A389446 a(n) = gcd(sigma(n), A057723(n)), where A057723 is sum of positive divisors of n that are divisible by every prime that divides n and sigma is the sum of divisors function.

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 6, 1, 2, 1, 6, 1, 2, 1, 14, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 6, 1, 6, 6, 2, 1, 2, 1, 3, 3, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 4, 1, 1, 6, 1, 6, 3, 2, 1, 3, 1, 2, 2, 2, 1, 6, 1, 6, 1, 2, 1, 14, 1, 2, 3, 2, 1, 6, 7, 6, 1, 2, 5, 6, 1, 1, 12, 1, 1, 6, 1, 14, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n).

Formula

a(n) = gcd(A000203(n), A308135(n)) = gcd(A057723(n), A308135(n)).

a(n) = A000203(n) / A389447(n).

a(n) = A057723(n) / A389448(n).

Mathematica

A389446[n_] := GCD[DivisorSigma[1, n], #*DivisorSigma[1, n/#]] & [Times @@ FactorInteger[n][[All, 1]]];
Array[A389446, 100] (* Paolo Xausa, Oct 07 2025 *)

Prog

(PARI)
A057723(n) = { my(f=factor(n)); prod(i=1, #f~, sigma(f[i, 1]^f[i, 2])-1); };
A389446(n) = gcd(sigma(n), A057723(n));

Crossrefs

Cf. A000203, A057723, A308135, A389447, A389448.

Sequence in context: A344877 A356156 A356157 * A333461 A325975 A325813

Adjacent sequences: A389443 A389444 A389445 * A389447 A389448 A389449

Keyword

nonn

Author

Antti Karttunen, Oct 04 2025

Status

approved