A180492 Product of remainders of prime(n) mod k, for k = 2,3,4,...,prime(n)-1.

1, 1, 2, 6, 720, 2160, 2419200, 65318400, 754427520000, 32953394073600000, 311409573995520000, 37269497815783833600000, 7890485108998805913600000000, 1096106738916569123487744000000, 4067286739206415827555188736000000000, 7924734685010508814047938347008000000000000

Offset: 1

Author

Carl R. White, Sep 08 2010

Keywords

• nonn

Comments

Nonzero entries in A180491. Note that this sequence, while increasing in general, is not strictly increasing.

a(n) is divisible by (n-1)!. - Robert G. Wilson v, Sep 09 2010

Examples

			Since prime(4) = 7, a(4) = (7 mod 2) * (7 mod 3) * (7 mod 4) * (7 mod 5) * (7 mod 6) = 1 * 1 * 3 * 2 * 1 = 6.
		

Crossrefs

Cf. A034386, A000142, A004125, A180491, A180493.

Cf. A173392, A000040.

Programs

Maple

a:= n-> (p-> mul(irem(p, k), k=2..p-1))(ithprime(n)):
seq(a(n), n=1..17);  # Alois P. Heinz, Jul 16 2022

Mathematica

f[n_]:=Times@@(Mod[n,# ]&/@ Range[2,n-1]); Table[f[Prime[i]],{i,20}] (* Harvey P. Dale, Sep 18 2010 *)
f[n_] := Times @@ Mod[n, Range[2, n - 1]]; Table[ f@ Prime@ n, {n, 10}] (* Robert G. Wilson v, Sep 09 2010 *)

Formula

a(n) = A173392(A000040(n)) = A180491(A000040(n)). - Ridouane Oudra, Nov 01 2024