A066727 Least factor of n^phi(n) - 1.

0, 1, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 17, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 13, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3

Offset: 1

Author

Robert G. Wilson v, Jan 15 2002

Keywords

• nonn

Comments

n^Phi(n)-1 is never prime. This sequence is an outgrowth of Euler's generalization to Fermat's little theorem.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A020639, A066916, A066699.

Programs

Mathematica

a = {}; Do[ a = Append[a, FactorInteger[ n^EulerPhi[n] - 1, FactorComplete -> False][[1, 1]]], {n, 1, 100}]; a

PARI

A020639(n) = if(1==n,n,forprime(p=2,,if(!(n%p),return(p))));
A066727(n) = if(1==n,0,A020639((n^eulerphi(n))-1)); \\ Antti Karttunen, Oct 24 2024

Formula

For n > 1, a(n) = A020639(A066916(n)). - Antti Karttunen, Oct 24 2024