A082055 Product of common prime-divisors (without multiplicity) of sigma(n) and phi(n).

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 6, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 1, 2, 2, 6, 1, 2, 6, 2, 2, 2, 6, 2, 2, 6, 2, 2, 2, 3, 1, 2, 2, 2, 6, 2, 6, 2, 2, 2, 2, 2, 6, 2, 1, 6, 2, 2, 2, 2, 6, 2, 3, 2, 6, 2, 2, 6, 6, 2, 2, 1, 2, 2, 2, 2, 6, 2, 10, 2, 6, 2, 2, 2, 2, 6, 2, 2, 3, 6, 1, 2, 2, 2, 6, 6

Offset: 1

Author

Labos Elemer, Apr 03 2003

Keywords

• nonn

Comments

The squarefree kernel of the greatest common divisor of sigma(n) and phi(n). - Antti Karttunen, Jan 22 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000203, A000010, A007947, A009223, A081396, A082054.

Programs

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[Times, Intersection[ba[EulerPhi[w]], ba[DivisorSigma[1, w]]]], {w, 1, 256}]

PARI

A082055(n) = factorback(factorint(gcd(sigma(n), eulerphi(n)))[, 1]); \\ Antti Karttunen, Jan 22 2020

Formula

a(n) = A007947(A009223(n)). - Antti Karttunen, Jan 22 2020