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.

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, 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, 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

Offset: 1

Author

Juri-Stepan Gerasimov, May 27 2023

Keywords

• nonn

Comments

The product of the multiplicities of distinct values of the n-th row of A102190.

Examples

			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.
		

Crossrefs

Cf. A000010, A102190, A348158.

Programs

Mathematica

a[n_] := Times @@ Tally[EulerPhi[Divisors[n]]][[;; , 2]]; Array[a, 100] (* Amiram Eldar, May 27 2023 *)

PARI

a(n)=my(f=vector(n)); fordiv(n,d,f[eulerphi(d)]++); vecprod([t | t<-f, t>0]) \\ Andrew Howroyd, May 27 2023