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

1,5

Links

Table of n, a(n) for n=1..77.

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002061, A130032.

Sequence in context: A283386 A278385 A245626 * A233320 A163535 A288395

Adjacent sequences: A307230 A307231 A307232 * A307234 A307235 A307236

Keyword

nonn,easy

Author

Jinyuan Wang, Apr 14 2019

Status

approved