

A323024


Numbers with exactly three distinct exponents in their prime factorization, or three distinct parts in their prime signature.


9



360, 504, 540, 600, 720, 756, 792, 936, 1008, 1176, 1188, 1200, 1224, 1350, 1368, 1400, 1404, 1440, 1500, 1584, 1620, 1656, 1836, 1872, 1960, 2016, 2052, 2088, 2160, 2200, 2232, 2250, 2268, 2352, 2400, 2448, 2484, 2520, 2600, 2646, 2664, 2736, 2800, 2880, 2904
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OFFSET

1,1


COMMENTS

Positions of 3's in A071625.
Numbers k such that A001221(A181819(k)) = 3.
The asymptotic density of this sequence is (6/Pi^2) * Sum_{n>=2, n squarefree} r(n)/((n1)*psi(n)) = 0.030575..., where psi is the Dedekind psi function (A001615), and r(n) = Sum_{dn, 1<d<n} 1/(d1) (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

Cf. A001221, A001222, A001615, A006939, A033992, A059404, A062770, A071625, A118914, A181819, A323014, A323022, A323025.
Sequence in context: A137487 A069478 A060665 * A072414 A163569 A063067
Adjacent sequences: A323021 A323022 A323023 * A323025 A323026 A323027


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jan 02 2019


STATUS

approved



