A348987 a(n) = gcd(sigma(n), A332994(n)).

1, 3, 4, 7, 6, 3, 8, 15, 13, 1, 12, 1, 14, 1, 1, 31, 18, 3, 20, 3, 1, 1, 24, 3, 31, 1, 40, 7, 30, 3, 32, 63, 1, 1, 1, 1, 38, 1, 1, 5, 42, 3, 44, 3, 2, 1, 48, 1, 57, 3, 1, 1, 54, 3, 1, 1, 1, 1, 60, 1, 62, 1, 4, 127, 1, 3, 68, 3, 1, 1, 72, 3, 74, 1, 2, 1, 1, 3, 80, 3, 121, 1, 84, 1, 1, 1, 1, 1, 90, 117, 1, 3, 1, 1, 1, 3

Offset: 1

Author

Antti Karttunen, Nov 06 2021

Keywords

• nonn

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A332994, A333784, A348988, A348989.

Cf. also A348977.

Programs

Mathematica

f[n_] := n/FactorInteger[n][[-1, 1]]; g[1] = 1; g[n_] := g[n] = n + g[f[n]]; a[n_] := GCD[g[n], DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Nov 06 2021 *)

PARI

A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));
A348987(n) = gcd(sigma(n), A332994(n));

Formula

a(n) = gcd(A000203(n), A332994(n)).

a(n) = gcd(A000203(n), A333784(n)) = gcd(A332994(n), A333784(n)).

a(n) = A332994(n) / A348988(n) = A000203(n) / A348989(n).