A082070 Smallest prime that divides phi(n) and sigma(n) = A000203(n), or 1 if phi(n) and sigma(n) are relatively prime.

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 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. A000010, A000203, A009223, A020639.

Cf. also A082064, A082067, A082068, A082069, A082071, A082072.

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_] := EulerPhi[x]; f2[x_] := DivisorSigma[1, 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}]]] & @@ {EulerPhi@ #, DivisorSigma[1, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

PARI

A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
A082070(n) = A020639(gcd(eulerphi(n),sigma(n))); \\ Antti Karttunen, Nov 03 2017

Formula

a(n) = A020639(A009223(n)). - Antti Karttunen, Nov 03 2017

Extensions

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