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

1,2

Comments

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

Links

Table of n, a(n) for n=1..90.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A102190, A348158.

Sequence in context: A327404 A360112 A333570 * A351032 A280726 A256607

Adjacent sequences: A363317 A363318 A363319 * A363321 A363322 A363323

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 27 2023

Status

approved