cp's OEIS Frontend

A082057 Least x=a(n) such that product of common prime-divisors [without multiplicity] of sigma(x) and phi(x) equals n; or 0 if n is not a squarefree number or if no such x exists. Among indices n only squarefree numbers arise because multiplicity of prime factors is ignored.

%I A082057 #12 Mar 27 2020 13:05:03
%S A082057 1,3,18,0,200,14,3364,0,0,88,9801,0,25281,116,1800,0,36992,0,4414201,
%T A082057 0,196,2881,541696,0,0,711,0,0,98942809,209,1547536,0,19602,6901,
%U A082057 814088,0,49042009,8473,1521,0,3150464641,377,245178368,0,0,6439,9265217536,0,0
%N A082057 Least x=a(n) such that product of common prime-divisors [without multiplicity] of sigma(x) and phi(x) equals n; or 0 if n is not a squarefree number or if no such x exists. Among indices n only squarefree numbers arise because multiplicity of prime factors is ignored.
%F A082057 a(n) = Min{x; A082055(x)=n}; 0 if n is not squarefree.
%e A082057 For n = 85: a(85) = 924800 = 128*5*5*17*17; sigma(924800) = 2426835 = 3*5*17*31*307; phi(924800) = 348160 = 4096*5*17; common prime factor 5.17 = 85.
%t A082057 ffi[x_] := Flatten[FactorInteger[x]]
%t A082057 lf[x_] := Length[FactorInteger[x]]
%t A082057 ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]
%t A082057 t=Table[0, {100}]; Do[s=Apply[Times, Intersection
%t A082057 [ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]];
%t A082057 If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t
%Y A082057 Cf. A000203, A000010, A082054, A082055, A082056.
%Y A082057 Cf. A073815.
%K A082057 nonn
%O A082057 1,2
%A A082057 _Labos Elemer_, Apr 03 2003
%E A082057 Corrected and extended by _David Wasserman_, Aug 27 2004