cp's OEIS Frontend

A108500 Number of values of k (1<=k<=n) where k^(n+1) != k mod n, or equivalently where sum_i{1<=i<=n} k^i != 0 mod n.

%I A108500 #3 Mar 30 2012 18:51:39
%S A108500 0,0,1,1,3,0,5,3,5,4,9,3,11,8,11,7,15,4,17,5,13,16,21,9,19,20,17,19,
%T A108500 27,12,29,15,29,28,31,15,35,32,31,15,39,0,41,35,37,40,45,21,41,28,47,
%U A108500 37,51,16,43,41,49,52,57,15,59,56,47,31,61,48,65,53,65,52,69,37,71,68,63,67
%N A108500 Number of values of k (1<=k<=n) where k^(n+1) != k mod n, or equivalently where sum_i{1<=i<=n} k^i != 0 mod n.
%F A108500 a(n)=n-A108499(n). a(n)=0 iff n is in A014117. a(p)=p-2 for p prime.
%e A108500 a(2)=0 since 1^3 = 1 mod 2 and 2^3 = 8 = 0 mod 2 = 2 mod 2.
%e A108500 a(3)=1 since 2^1+2^2+2^3 = 14 = 2 mod 3 != 0 mod 3 but 1^1+1^2+1^3 = 3 = 0 mod 3 and 3^1+3^2+3^3 = 39 = 0 mod 3.
%Y A108500 Numbers of nonzeros in rows of A108497 or A108498.
%K A108500 nonn
%O A108500 1,5
%A A108500 _Henry Bottomley_, Jun 06 2005