A197113 Nonprime numbers n such that the greatest residue of the congruence x^n (mod n) equals n-1 where x = 0..n-1.

1, 9, 10, 15, 21, 25, 26, 27, 33, 34, 35, 39, 45, 49, 50, 51, 55, 57, 58, 63, 65, 69, 74, 75, 77, 81, 82, 85, 87, 91, 93, 95, 99, 105, 106, 111, 115, 117, 119, 121, 122, 123, 125, 129, 130, 133, 135, 141, 143, 145, 146, 147, 153, 155, 159, 161, 165, 169, 170

Offset

1,2

Comments

Subset of A196499.

For all primes n, the greatest residue of the congruence x^n (mod n) where x = 0..n-1 equals n-1.

Links

Table of n, a(n) for n=1..59.

Example

50 is in the sequence because the residues of the congruence x^50 (mod 50) are { 0, 1, 24, 25, 26, 49} and the greatest value is 50 - 1 = 49.

Maple

with(numtheory):T:=array(1..170): for n from 1 to 170 do:for k from 1 to n do:T[k]:=irem(k^n, n):od:W:=convert(T, set):x:=nops(W):if type(n, prime) = false and W[x]= n-1 then printf(`%d, `, n):else fi:od:

Crossrefs

Cf. A196499, A196082.

Sequence in context: A005381 A175090 A365166 * A099616 A073829 A003135

Adjacent sequences: A197110 A197111 A197112 * A197114 A197115 A197116

Keyword

nonn

Author

Michel Lagneau, Oct 13 2011

Status

approved