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a(n) = Product_{d|n} psi(d), where psi(m) is the sum of totatives of m (A023896).
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%I #8 Sep 08 2022 08:46:18

%S 1,1,3,4,10,18,21,64,81,200,55,1728,78,882,1800,4096,136,26244,171,

%T 64000,7938,6050,253,2654208,2500,12168,19683,592704,406,25920000,465,

%U 1048576,54450,36992,88200,544195584,666,58482,109512,327680000,820,504094752,903

%N a(n) = Product_{d|n} psi(d), where psi(m) is the sum of totatives of m (A023896).

%C a(n) = n only for n = 1, 3 and 4.

%C n divides a(n) for all n except 2.

%C Conjecture: a(n) is odd iff the sum of totatives of n (A023896) is odd.

%F a(n) = Product_{d|n} A023896(d).

%e For n=6; sets of totatives of divisors of 6: {1}, {1}, {1, 2}, {1, 5}; a(6) = 1*1*(1+2)*(1+5) = 18.

%t Table[Product[Total@ Select[Range@ d, CoprimeQ[d, #] &], {d, Divisors@ n}], {n, 43}] (* _Michael De Vlieger_, Dec 30 2016 *)

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

%Y Cf. A023896, A057661, A280247, A280248.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Dec 30 2016