A108499 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.

1, 2, 2, 3, 2, 6, 2, 5, 4, 6, 2, 9, 2, 6, 4, 9, 2, 14, 2, 15, 8, 6, 2, 15, 6, 6, 10, 9, 2, 18, 2, 17, 4, 6, 4, 21, 2, 6, 8, 25, 2, 42, 2, 9, 8, 6, 2, 27, 8, 22, 4, 15, 2, 38, 12, 15, 8, 6, 2, 45, 2, 6, 16, 33, 4, 18, 2, 15, 4, 18, 2, 35, 2, 6, 12, 9, 4, 42, 2, 45, 28, 6, 2, 63, 4, 6, 4, 15, 2, 42, 4

Offset: 1

Author

Henry Bottomley, Jun 06 2005

Keywords

• nonn

Examples

			a(2)=2 since 1^3 = 1 mod 2 and 2^3 = 8 = 0 mod 2 = 2 mod 2.
a(3)=2 since 1^1+1^2+1^3 = 3 = 0 mod 3 and 3^1+3^2+3^3 = 39 = 0 mod 3 but 2^1+2^2+2^3 = 14 = 2 mod 3 != 0 mod 3.
		

Crossrefs

Numbers of zeros in rows of A108497 or A108498.

Formula

a(n)=n-A108500(n). a(n)=n iff n is in A014117.