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.

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, 27, 12, 29, 15, 29, 28, 31, 15, 35, 32, 31, 15, 39, 0, 41, 35, 37, 40, 45, 21, 41, 28, 47, 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

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Formula

a(n)=n-A108499(n). a(n)=0 iff n is in A014117. a(p)=p-2 for p prime.

Example

a(2)=0 since 1^3 = 1 mod 2 and 2^3 = 8 = 0 mod 2 = 2 mod 2.
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.

Crossrefs

Numbers of nonzeros in rows of A108497 or A108498.

Sequence in context: A088191 A179179 A291503 * A322937 A326989 A326937

Adjacent sequences: A108497 A108498 A108499 * A108501 A108502 A108503

Keyword

nonn

Author

Henry Bottomley, Jun 06 2005

Status

approved