A348989 Denominator of A332994(n) / sigma(n).

1, 1, 1, 1, 1, 4, 1, 1, 1, 18, 1, 28, 1, 24, 24, 1, 1, 13, 1, 14, 32, 36, 1, 20, 1, 42, 1, 8, 1, 24, 1, 1, 48, 54, 48, 91, 1, 60, 56, 18, 1, 32, 1, 28, 39, 72, 1, 124, 1, 31, 72, 98, 1, 40, 72, 120, 80, 90, 1, 168, 1, 96, 26, 1, 84, 48, 1, 42, 96, 144, 1, 65, 1, 114, 62, 140, 96, 56, 1, 62, 1, 126, 1, 224, 108, 132, 120

Offset: 1

Author

Antti Karttunen, Nov 06 2021

Keywords

• nonn
• frac

Comments

See comments in A348988.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A332994, A333784, A348987, A348988 (numerators).

Cf. also A348978, A348979.

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

A332994(n) = if(1==n,n,n + A332994(n/vecmax(factor(n)[,1])));
A348989(n) = { my(s=sigma(n)); (s/gcd(s, A332994(n))); };

Formula

a(n) = A000203(n) / A348987(n) = A000203(n) / gcd(A000203(n), A332994(n)).