A082072 Smallest prime that divides sigma(n) = A000203(n) and sigma_2(n) = A001157(n), or 1 if sigma(n) and sigma_2(n) are relatively prime.

1, 1, 2, 7, 2, 2, 2, 5, 13, 2, 2, 2, 2, 2, 2, 31, 2, 13, 2, 2, 2, 2, 2, 2, 31, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 127, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 7, 2, 2

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000203, A001157, A020639, A179931.

Cf. also A082066, A082067, A082068, A082069, A082070, A082071.

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]}]; f1[x_] := DivisorSigma[1, x]; f2[x_] := DivisorSigma[2, x]; Table[Min[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
(* Second program: *)
Array[If[CoprimeQ[#1, #2], 1, Min@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {DivisorSigma[1, #], DivisorSigma[2, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

PARI

lpf(n)=my(f=factor(n)[,1]); if(#f,f[1],1)
a(n)=lpf(gcd(sigma(n),sigma(n,2))) \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = A020639(A179931(n)). - Antti Karttunen, Nov 03 2017

Extensions

Name edited by Antti Karttunen after an example by N. J. A. Sloane, Nov 04 2017