A197928 Number of pairs of integers i,j with 1<=i<=n, 1<=j<=i, such that i^2-j^2 = i*j (mod n).

1, 1, 1, 3, 3, 1, 1, 3, 6, 3, 11, 3, 1, 1, 3, 10, 1, 6, 19, 11, 1, 11, 1, 3, 15, 1, 6, 3, 29, 3, 31, 10, 11, 1, 3, 21, 1, 19, 1, 11, 41, 1, 1, 43, 24, 1, 1, 10, 28, 15, 1, 3, 1, 6, 53, 3, 19, 29, 59, 11, 61, 31, 6, 36, 3, 11, 1, 3, 1, 3, 71, 21, 1, 1, 15, 75, 11, 1, 79, 42, 45, 41, 1, 3, 3, 1, 29, 43, 89, 24, 1, 3, 31, 1, 93, 10, 1, 28, 96, 55, 101, 1, 1, 3, 3

Offset

1,4

Comments

It appears that, except for the first term, a(n)=n if and only if n is a prime congruent to 1 or 4 (mod 5).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maple

a:= n-> add(add(`if`(irem((i-j)*(i+j)-i*j, n)=0, 1, 0), j=1..i), i=1..n):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 19 2011

Crossrefs

Cf. A180783.

Sequence in context: A090569 A160324 A347026 * A109439 A247646 A133333

Adjacent sequences: A197925 A197926 A197927 * A197929 A197930 A197931

Keyword

nonn

Author

John W. Layman, Oct 19 2011

Status

approved