A082054 Sum of common prime divisors (without multiplicity) of sigma(n) and phi(n).

0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 5, 2, 0, 2, 3, 2, 2, 2, 2, 2, 2, 0, 5, 2, 2, 2, 2, 2, 0, 2, 2, 5, 0, 2, 5, 2, 2, 2, 5, 2, 2, 5, 2, 2, 2, 3, 0, 2, 2, 2, 5, 2, 5, 2, 2, 2, 2, 2, 5, 2, 0, 5, 2, 2, 2, 2, 5, 2, 3, 2, 5, 2, 2, 5, 5, 2, 2, 0, 2, 2, 2, 2, 5, 2, 7, 2, 5, 2, 2, 2, 2, 5, 2, 2, 3, 5, 0, 2, 2, 2, 5, 5

Offset

1,3

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A008472(A009223(n)). - Amiram Eldar, Feb 16 2025

Mathematica

ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; Table[Apply[Plus, Intersection[ba[EulerPhi[w]], ba[DivisorSigma[1, w]]]], {w, 1, 256}]
a[n_] := Module[{g = GCD[DivisorSigma[1, n], EulerPhi[n]]}, If[g == 1, 0, Total[FactorInteger[g][[;; , 1]]]]]; Array[a, 100] (* Amiram Eldar, Feb 16 2025 *)

Prog

(PARI) a(n)=my(f=factor(gcd(sigma(n=factor(n)), eulerphi(n)))[, 1]); sum(i=1, #f, f[i]) \\ Charles R Greathouse IV, Dec 09 2013

Crossrefs

Cf. A000010, A000203, A008472, A009223.

Sequence in context: A350151 A341846 A262670 * A327276 A044943 A292118

Adjacent sequences: A082051 A082052 A082053 * A082055 A082056 A082057

Keyword

nonn

Author

Labos Elemer, Apr 03 2003

Status

approved