%I #14 Jul 15 2023 05:59:32
%S 1,2,1,2,1,4,1,2,1,4,1,6,1,4,1,2,1,8,1,4,1,4,1,12,1,4,1,4,1,16,1,2,1,
%T 4,1,12,1,4,1,6,1,16,1,4,1,4,1,24,1,8,1,4,1,16,1,4,1,4,1,54,1,4,2,2,1,
%U 16,1,4,1,16,1,24,1,4,1,4,1,16,1,12,1,4,1,36,1,4,1,4,1,64
%N a(n) is the product of the frequencies of the distinct values obtained when the Euler totient function is applied to the divisors of n.
%C The product of the multiplicities of distinct values of the n-th row of A102190.
%e The divisors of 12 are {1, 2, 3, 4, 6, 12} and their phi values are {1, 1, 2, 2, 2, 4} whose sum is also 12. The set of distinct values are {1, 2, 4} which occur with multiplicities {2, 3, 1} respectively. Therefore, a(12) = 2*3*1 = 6.
%t a[n_] := Times @@ Tally[EulerPhi[Divisors[n]]][[;; , 2]]; Array[a, 100] (* _Amiram Eldar_, May 27 2023 *)
%o (PARI) a(n)=my(f=vector(n)); fordiv(n,d,f[eulerphi(d)]++); vecprod([t | t<-f, t>0]) \\ _Andrew Howroyd_, May 27 2023
%Y Cf. A000010, A102190, A348158.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, May 27 2023