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.

1, 3, 18, 0, 200, 14, 3364, 0, 0, 88, 9801, 0, 25281, 116, 1800, 0, 36992, 0, 4414201, 0, 196, 2881, 541696, 0, 0, 711, 0, 0, 98942809, 209, 1547536, 0, 19602, 6901, 814088, 0, 49042009, 8473, 1521, 0, 3150464641, 377, 245178368, 0, 0, 6439, 9265217536, 0, 0

Offset: 1

Author

Labos Elemer, Apr 03 2003

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000203, A000010, A082054, A082055, A082056.

Cf. A073815.

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]}]
t=Table[0, {100}]; Do[s=Apply[Times, Intersection
[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]];
If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t

Formula

a(n) = Min{x; A082055(x)=n}; 0 if n is not squarefree.

Extensions

Corrected and extended by David Wasserman, Aug 27 2004