This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180492 #17 Jun 02 2025 03:04:05
%S A180492 1,1,2,6,720,2160,2419200,65318400,754427520000,32953394073600000,
%T A180492 311409573995520000,37269497815783833600000,
%U A180492 7890485108998805913600000000,1096106738916569123487744000000,4067286739206415827555188736000000000,7924734685010508814047938347008000000000000
%N A180492 Product of remainders of prime(n) mod k, for k = 2,3,4,...,prime(n)-1.
%C A180492 Nonzero entries in A180491. Note that this sequence, while increasing in general, is not strictly increasing.
%C A180492 a(n) is divisible by (n-1)!. - _Robert G. Wilson v_, Sep 09 2010
%F A180492 a(n) = A173392(A000040(n)) = A180491(A000040(n)). - _Ridouane Oudra_, Nov 01 2024
%e A180492 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.
%p A180492 a:= n-> (p-> mul(irem(p, k), k=2..p-1))(ithprime(n)):
%p A180492 seq(a(n), n=1..17); # _Alois P. Heinz_, Jul 16 2022
%t A180492 f[n_]:=Times@@(Mod[n,# ]&/@ Range[2,n-1]); Table[f[Prime[i]],{i,20}] (* _Harvey P. Dale_, Sep 18 2010 *)
%t A180492 f[n_] := Times @@ Mod[n, Range[2, n - 1]]; Table[ f@ Prime@ n, {n, 10}] (* _Robert G. Wilson v_, Sep 09 2010 *)
%Y A180492 Cf. A034386, A000142, A004125, A180491, A180493.
%Y A180492 Cf. A173392, A000040.
%K A180492 nonn
%O A180492 1,3
%A A180492 _Carl R. White_, Sep 08 2010