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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 (list; graph; refs; listen; history; text; internal format)
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

n = 85: a(n) = 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 = n.

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-A082056.

Cf. A073815.

Sequence in context: A161473 A208493 A082056 * A161687 A245498 A120647

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

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Last modified January 27 15:14 EST 2020. Contains 331295 sequences. (Running on oeis4.)