A307233 a(n) = Product_{k=1..n} (k^2 + k + 1) mod n.

0, 1, 0, 1, 3, 3, 0, 1, 0, 9, 3, 9, 0, 7, 12, 1, 3, 9, 0, 1, 0, 9, 3, 9, 18, 13, 0, 21, 3, 9, 0, 1, 27, 9, 7, 9, 0, 19, 0, 1, 3, 21, 0, 37, 18, 9, 3, 33, 0, 49, 27, 13, 3, 27, 12, 49, 0, 9, 3, 21, 0, 31, 0, 1, 13, 3, 0, 13, 27, 49, 3, 9, 0, 37, 57, 57, 42

Offset: 1

Author

Jinyuan Wang, Apr 14 2019

Keywords

• nonn
• easy

Examples

			a(4) = 1 since 3*7*13*21 = 1 mod 4.
		

Crossrefs

Cf. A002061, A130032.

Programs

Mathematica

Table[Mod[Product[k^2+k+1, {k, 0, n}], n], {n, 1, 100}]

PARI

a(n) = prod(k=1, n, k^2+k+1) % n

Formula

a(n) = A130032(n) mod n.

If prime p == 1 mod 3, a(p) = 0; if p == 2 mod 3, a(p) = 3 for prime p > 3.

a(A002061(k)) = 0.

If a(j) = a(k) = 0, then a(j*k) = 0.