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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.
0
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved