A173392 -id:A173392 - cp's OEIS frontend

A180491 Product of remainders of n mod k, for k = 2,3,4,...,n-1.

1, 1, 1, 0, 2, 0, 6, 0, 0, 0, 720, 0, 2160, 0, 0, 0, 2419200, 0, 65318400, 0, 0, 0, 754427520000, 0, 0, 0, 0, 0, 32953394073600000, 0, 311409573995520000, 0, 0, 0, 0, 0, 37269497815783833600000, 0, 0, 0, 7890485108998805913600000000, 0

Offset: 1

Carl R. White, Sep 08 2010

nonn

a(n) is zero where n is composite and is trivially less than or equal to n! when n is prime or 1.

a(n)=0 iff n is composite. See A180492. - Robert G. Wilson v, Sep 09 2010

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

Cf. A034386, A000142, A004125, A180492, A180493.

Cf. A080339, A173392.

a:=proc(n) if n=1 then 1; elif isprime(n)=true then mul(n mod i, i=2..n-1); else 0; fi: end: seq(a(n), n=1..60); # Ridouane Oudra, Nov 01 2024

f[n_] := Times @@ Mod[n, Range[2, n - 1]]; Array[f, 42] (* Robert G. Wilson v, Sep 09 2010 *)

a(n) = A080339(n)*A173392(n). - Ridouane Oudra, Nov 01 2024

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

Original entry on oeis.org

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

Offset: 1

Carl R. White, Sep 08 2010

nonn

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

			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.

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

Cf. A173392, A000040.

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

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 *)

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

cp's OEIS Frontend

A180491 Product of remainders of n mod k, for k = 2,3,4,...,n-1.

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