login
A066727
Least factor of n^phi(n) - 1.
2
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
1,3
COMMENTS
n^Phi(n)-1 is never prime. This sequence is an outgrowth of Euler's generalization to Fermat's little theorem.
LINKS
FORMULA
For n > 1, a(n) = A020639(A066916(n)). - Antti Karttunen, Oct 24 2024
MATHEMATICA
a = {}; Do[ a = Append[a, FactorInteger[ n^EulerPhi[n] - 1, FactorComplete -> False][[1, 1]]], {n, 1, 100}]; a
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jan 15 2002
STATUS
approved