cp's OEIS Frontend

A280821 Partial products of A001783.

%I A280821 #35 Aug 16 2025 06:21:05
%S A280821 1,1,2,6,144,720,518400,54432000,121927680000,23044331520000,
%T A280821 83623270219776000000,32194959034613760000000,
%U A280821 15421436889514446422016000000000,297710839152076388177018880000000000,267015660792140704250415525396480000000000
%N A280821 Partial products of A001783.
%C A280821 A001783(n) = the product of totatives of n.
%H A280821 Project Euler, <a href="https://projecteuler.net/problem=754">Problem 754: Product of Gauss Factorials</a>.
%F A280821 a(n) = Product_{i=1..n} A001783(i).
%F A280821 a(n) = A000178(n)/A281027(n). - _Amiram Eldar_, Aug 16 2025
%t A280821 FoldList[#1 #2 &, Table[Times @@ Select[Range@ n, CoprimeQ[n, #] &], {n, 15}]] (* _Michael De Vlieger_, Jan 11 2017 *)
%t A280821 SetAttributes[Phitorial,{Listable}]
%t A280821 Phitorial[n_]:=n^EulerPhi[n]*Times@@((Factorial[#]/#^#)^MoebiusMu[n/#]&/@Divisors[n])
%t A280821 FoldList[Times,Phitorial[Range[20]]] (* _Peter Cullen Burbery_, Jul 14 2023 *)
%o A280821 (Magma) [&*[&*[h: h in [1..k] | GCD(h,k) eq 1]: k in [1..n]]: n in [1..100]];
%o A280821 (PARI) f(n) = prod(k=2, n-1, k^(gcd(k, n)==1)); \\ A001783
%o A280821 a(n) = prod(i=1, n, f(i)); \\ _Michel Marcus_, Jul 14 2023
%Y A280821 Cf. A000178, A001783, A280820, A281027.
%K A280821 nonn
%O A280821 1,3
%A A280821 _Jaroslav Krizek_, Jan 11 2017