A066916 -id:A066916 - cp's OEIS frontend

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

Robert G. Wilson v, Jan 15 2002

nonn

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

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

Cf. A000010, A020639, A066916, A066699.

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

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

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

A066915 a(n) = n^phi(n) + 1.

Original entry on oeis.org

2, 3, 10, 17, 626, 37, 117650, 4097, 531442, 10001, 25937424602, 20737, 23298085122482, 7529537, 2562890626, 4294967297, 48661191875666868482, 34012225, 104127350297911241532842, 25600000001, 7355827511386642, 26559922791425, 907846434775996175406740561330, 110075314177

Offset: 1

Jason Earls, Jan 23 2002

nonn

Harry J. Smith, Table of n, a(n) for n = 1..100

Cf. A000010, A062981, A066719, A066916.

Table[n^EulerPhi[n]+1,{n,30}] (* Harvey P. Dale, May 29 2014 *)

a(n) = { n^eulerphi(n) + 1 } \\ Harry J. Smith, Apr 06 2010

a(n) = A062981(n) + 1.

cp's OEIS Frontend

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

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