cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

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.

Original entry on oeis.org

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

Views

Author

Labos Elemer, Apr 03 2003

Keywords

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

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
Showing 1-1 of 1 results.