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

1,2

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

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.

Sequence in context: A015995 A068903 A329607 * A260895 A107753 A197929

Adjacent sequences: A108496 A108497 A108498 * A108500 A108501 A108502

Keyword

nonn

Author

Henry Bottomley, Jun 06 2005

Status

approved