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 A363320 #14 Jul 15 2023 05:59:32 %S A363320 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 A363320 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 A363320 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 A363320 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 A363320 The product of the multiplicities of distinct values of the n-th row of A102190. %e A363320 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 A363320 a[n_] := Times @@ Tally[EulerPhi[Divisors[n]]][[;; , 2]]; Array[a, 100] (* _Amiram Eldar_, May 27 2023 *) %o A363320 (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 A363320 Cf. A000010, A102190, A348158. %K A363320 nonn %O A363320 1,2 %A A363320 _Juri-Stepan Gerasimov_, May 27 2023