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

1,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000010, A001157, A020639.

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

Sequence in context: A347342 A304943 A248597 * A082065 A082070 A336648

Adjacent sequences: A082068 A082069 A082070 * A082072 A082073 A082074

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

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

Status

approved