A348979 Denominator of ratio A332993(n) / sigma(n).

1, 1, 1, 1, 1, 6, 1, 1, 1, 9, 1, 14, 1, 12, 8, 1, 1, 39, 1, 7, 32, 18, 1, 30, 1, 21, 1, 28, 1, 24, 1, 1, 16, 27, 48, 91, 1, 30, 56, 45, 1, 96, 1, 14, 13, 36, 1, 62, 1, 31, 24, 49, 1, 60, 72, 60, 80, 45, 1, 56, 1, 48, 26, 1, 84, 48, 1, 21, 32, 144, 1, 195, 1, 57, 62, 70, 96, 168, 1, 31, 1, 63, 1, 224, 108, 66, 40, 90

Offset: 1

Author

Antti Karttunen, Nov 06 2021

Keywords

• nonn
• frac

Comments

See comments in A348978.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A332993, A333783, A348977, A348978 (numerators).

Cf. also A348988, A348989.

Programs

Mathematica

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

PARI

A332993(n) = if(1==n,n,n + A332993(n/vecmin(factor(n)[,1])));
A348979(n) = { my(s=sigma(n)); (s/gcd(s, A332993(n))); };

Formula

a(n) = A000203(n) / A348977(n) = A000203(n) / gcd(A000203(n), A332993(n)).