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

1,3

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

Links

Table of n, a(n) for n=1..16.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A110795 A179860 A067107 * A169661 A047690 A113569

Adjacent sequences: A180489 A180490 A180491 * A180493 A180494 A180495

Keyword

nonn

Author

Carl R. White, Sep 08 2010

Status

approved