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

1,3

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

Formula

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A123926 A336476 A082064 * A073812 A009223 A110244

Adjacent sequences: A082052 A082053 A082054 * A082056 A082057 A082058

Keyword

nonn

Author

Labos Elemer, Apr 03 2003

Status

approved