A389080 a(n) = gcd(sigma(n), A048250(n)), where sigma is the sum of divisors and A048250 is the sum of squarefree divisors.

1, 3, 4, 1, 6, 12, 8, 3, 1, 18, 12, 4, 14, 24, 24, 1, 18, 3, 20, 6, 32, 36, 24, 12, 1, 42, 4, 8, 30, 72, 32, 3, 48, 54, 48, 1, 38, 60, 56, 18, 42, 96, 44, 12, 6, 72, 48, 4, 1, 3, 72, 14, 54, 12, 72, 24, 80, 90, 60, 24, 62, 96, 8, 1, 84, 144, 68, 18, 96, 144, 72, 3, 74, 114, 4, 20, 96, 168, 80, 6, 1, 126, 84, 32, 108

Offset

1,2

Comments

First differs from A348503 at n = 72, from A344695 at n = 108, and from A367991 at n = 196.

Not multiplicative: a(4) = 1, a(49) = 1, but a(4*49) = a(196) = 3 <> 1*1.

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), A048250(n)).

a(n) = A000203(n) / A389087(n).

a(n) = A048250(n) / A389089(n).

Mathematica

a[n_]:=GCD[DivisorSigma[1, n], Total[Select[Divisors[n], SquareFreeQ]]]; Array[a, 85] (* James C. McMahon, Oct 07 2025 *)

Prog

(PARI)
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A389080(n) = gcd(sigma(n), A048250(n));

Crossrefs

Cf. A000203, A048250, A389087, A389089.

Cf. A323159, A344695, A348503, A367991.

Sequence in context: A389451 A367991 A344695 * A348503 A348047 A348984

Adjacent sequences: A389077 A389078 A389079 * A389081 A389082 A389083

Keyword

nonn

Author

Antti Karttunen, Oct 03 2025

Status

approved