Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jan 22 2020 20:08:52
%S 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,
%T 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,
%U 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
%N Product of common prime-divisors (without multiplicity) of sigma(n) and phi(n).
%C The squarefree kernel of the greatest common divisor of sigma(n) and phi(n). - _Antti Karttunen_, Jan 22 2020
%H Antti Karttunen, <a href="/A082055/b082055.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A007947(A009223(n)). - _Antti Karttunen_, Jan 22 2020
%t 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}]
%o (PARI) A082055(n) = factorback(factorint(gcd(sigma(n), eulerphi(n)))[, 1]); \\ _Antti Karttunen_, Jan 22 2020
%Y Cf. A000203, A000010, A007947, A009223, A081396, A082054.
%K nonn
%O 1,3
%A _Labos Elemer_, Apr 03 2003