A280821 - OEIS

%I #28 Jul 27 2023 19:19:16

%S 1,1,2,6,144,720,518400,54432000,121927680000,23044331520000,

%T 83623270219776000000,32194959034613760000000,

%U 15421436889514446422016000000000,297710839152076388177018880000000000,267015660792140704250415525396480000000000

%N Partial products of A001783.

%C A001783(n) = the product of totatives of n.

%H Project Euler, <a href="https://projecteuler.net/problem=754">Problem 754: Product of Gauss Factorials</a>.

%F a(n) = Product_{i=1..n} A001783(i).

%t FoldList[#1 #2 &, Table[Times @@ Select[Range@ n, CoprimeQ[n, #] &], {n, 15}]] (* _Michael De Vlieger_, Jan 11 2017 *)

%t SetAttributes[Phitorial,{Listable}]

%t Phitorial[n_]:=n^EulerPhi[n]*Times@@((Factorial[#]/#^#)^MoebiusMu[n/#]&/@Divisors[n])

%t FoldList[Times,Phitorial[Range[20]]] (* _Peter Cullen Burbery_, Jul 14 2023 *)

%o (Magma) [&*[&*[h: h in [1..k] | GCD(h,k) eq 1]: k in [1..n]]: n in [1..100]]

%o (PARI) f(n) = prod(k=2, n-1, k^(gcd(k, n)==1)); \\ A001783

%o a(n) = prod(i=1, n, f(i)); \\ _Michel Marcus_, Jul 14 2023

%Y Cf. A001783, A280820.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Jan 11 2017