A082071 Smallest common prime-divisor of phi(n) = A000010(n) and sigma_2(n) = A001157(n); a(n)=1 if no common prime-divisor exists.

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 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, A001157, A020639.

Cf. also A082065, A082067, A082068, A082069, A082070, A082072.

Programs

Mathematica

Array[If[CoprimeQ[#1, #2], 1, Min@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {EulerPhi@ #,
DivisorSigma[2, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)

PARI

A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
A082071(n) = A020639(gcd(eulerphi(n),sigma(n,2))); \\ Antti Karttunen, Nov 03 2017

Formula

a(n) = A020639(gcd(A000010(n), A001157(n))). - Antti Karttunen, Nov 03 2017

Extensions

Values corrected by R. J. Mathar, Jul 09 2011

More terms from Antti Karttunen, Nov 03 2017

Changed "was found" to "exists" in definition. - N. J. A. Sloane, Jan 29 2022