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

1,2

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

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.

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

Crossrefs

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

Cf. A073815.

Sequence in context: A161473 A208493 A082056 * A161687 A245498 A350703

Adjacent sequences: A082054 A082055 A082056 * A082058 A082059 A082060

Keyword

nonn

Author

Labos Elemer, Apr 03 2003

Extensions

Corrected and extended by David Wasserman, Aug 27 2004

Status

approved