A242111 - OEIS

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A242111

Number of nonnegative k such that k^2 + 2 divides n^2 + 2.

1, 1, 3, 1, 4, 2, 2, 2, 5, 1, 5, 2, 2, 2, 7, 1, 4, 2, 2, 3, 4, 1, 6, 2, 2, 3, 4, 1, 4, 2, 3, 2, 8, 1, 4, 2, 3, 2, 4, 1, 5, 4, 2, 2, 7, 1, 4, 3, 2, 3, 5, 1, 8, 2, 2, 2, 4, 1, 11, 3, 2, 3, 4, 2, 4, 2, 2, 2, 5, 2, 6, 3, 2, 2, 7, 1, 7, 2, 2, 2, 7, 1, 5, 2, 2, 3, 6, 1, 4, 2, 2, 3, 7, 1, 5, 4, 3, 2, 4, 1, 4, 2, 3, 3, 5, 1, 4, 3, 3, 3, 4, 1, 8, 4, 2, 2, 4, 1, 6, 2, 3, 2, 5, 1, 6, 2, 2, 2

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OFFSET

0,3

COMMENTS

a(A067201(n)) = 1, but these are not the only cases where a(k) = 1.

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Sum_{k>=0} (Sum_{i in S(k)} x^i)/(1 - x^(k^2+2)) where S(k) = {i : 0 <= i < k^2 + 2, i^2 + 2 == 0 (mod k^2 + 2)}.

EXAMPLE

For n=2, n^2+2=6 is divisible by 0^2+2=2, 1^2+2=3 and 2^2+2=6 so a(2)=3.

MAPLE