A082063 Greatest common prime divisor of n and sigma_2(n) = A001157(n), or 1 if the two are relatively prime.

1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 3, 1, 2, 5, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 7, 1, 5, 1, 1, 1, 2, 5, 3, 1, 2, 1, 5, 1, 2, 1, 2, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 2, 1, 2, 1, 5, 1, 2, 7, 1, 13, 2, 1, 2, 1, 5, 1, 1, 1, 2, 5, 2, 1, 2, 1, 2, 1, 2, 1, 7, 5, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 5

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A001157, A179930.

Cf. also A082061, A082062, A082064, A082065, A082066, A082069.

Programs

Mathematica

(* factors/exponent SET *) ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; f1[x_] := x; f2[x_] := DivisorSigma[2, x]; Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
(* Second program: *)
Array[If[CoprimeQ[#1, #2], 1, Max@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {#, DivisorSigma[2, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

PARI

A006530(n) = if(1==n, n, vecmax(factor(n)[, 1]));
A082063(n) = A006530(gcd(sigma(n,2), n)); \\ Antti Karttunen, Nov 03 2017

Formula

a(n) = A006530(A179930(n)). - Antti Karttunen, Nov 03 2017

Extensions

Erroneous comment removed by Antti Karttunen, Nov 03 2017