A196547 Nonprime numbers m such that the sum of the distinct residues of x^m (mod m) is divisible by m, x=0..m-1.

1, 9, 14, 15, 21, 22, 25, 27, 28, 30, 33, 35, 38, 39, 45, 46, 49, 51, 52, 55, 57, 62, 63, 65, 66, 69, 70, 75, 77, 78, 81, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 111, 115, 116, 117, 118, 119, 121, 123, 124, 125, 129, 132, 133, 134, 135, 138, 141, 142

Offset: 1

Author

Michel Lagneau, Oct 03 2011

Keywords

• nonn

Comments

Subset of A196546.

Examples

			a(3) = 14 because x^14 == 0, 1, 2, 4, 7, 8, 9, 11
(mod 14), and the sum  0+1+2+4+7+8+9+11 = 42 is divisible by 14.
		

Crossrefs

Cf. A195637, A196546.

Programs

Maple

with(numtheory):T:=array(1..150): for n from 1 to 150 do:for k from 1 to n do:T[k]:=irem(k^n,n):od:W:=convert(T,set):x:=nops(W):s:=0:for i from 1 to x do:s:=s+W[i]:od:if irem(s,n)=0 and type(n,prime)=false then printf(`%d, `,n):else fi:od: