OFFSET
1,12
COMMENTS
The number of permutations of the exponents in the prime signature of n.
The number of terms in the n-th row of A111470.
LINKS
FORMULA
EXAMPLE
a(12) = a(18) = 2 since 12 = 2^2 * 3 and 18 = 3^2 * 2 have the same prime signature, (2, 1), and the same set of distinct prime factors, {2, 3}.
a(60) = a(90) = a(150) = 3 since 60 = 2^2 * 3 * 5, 90 = 3^2 * 2 * 5, and 150 = 5^2 * 2 * 3 have the same prime signature, (2, 1, 1), and the same set of distinct prime factors, {2, 3, 5}.
MATHEMATICA
a[n_] := Multinomial @@ Tally[FactorInteger[n][[;; , 2]]][[;; , 2]]; Array[a, 100]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 22 2019
EXTENSIONS
More terms from Antti Karttunen, Sep 27 2019
STATUS
approved