OFFSET
1,1
COMMENTS
Positions of 3's in A071625.
The asymptotic density of this sequence is (6/Pi^2) * Sum_{n>=2, n squarefree} r(n)/((n-1)*psi(n)) = 0.030575..., where psi is the Dedekind psi function (A001615), and r(n) = Sum_{d|n, 1<d<n} 1/(d-1) (Sanna, 2020). - Amiram Eldar, Oct 18 2020
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Carlo Sanna, On the number of distinct exponents in the prime factorization of an integer, Proceedings - Mathematical Sciences, Indian Academy of Sciences, Vol. 130, No. 1 (2020), Article 27, alternative link.
EXAMPLE
1500 = 2^2 * 3^1 * 5^3 has three distinct exponents {1, 2, 3}, so belongs to the sequence.
52500 = 2^2 * 3^1 * 5^4 * 7^1 has three distinct exponents {1, 2, 4}, so belongs to the sequence.
MATHEMATICA
tom[n_]:=Length[Union[Last/@If[n==1, {}, FactorInteger[n]]]];
Select[Range[1000], tom[#]==3&]
PROG
(PARI) is(n) = #Set(factor(n)[, 2]) == 3 \\ David A. Corneth, Jan 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 02 2019
STATUS
approved