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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.
0
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 03 2003
EXTENSIONS
Corrected and extended by David Wasserman, Aug 27 2004
STATUS
approved