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

1,3

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A000203, A009223, A020639.

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

Sequence in context: A248597 A082071 A082065 * A336648 A082902 A123926

Adjacent sequences: A082067 A082068 A082069 * A082071 A082072 A082073

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Extensions

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

Status

approved