A375076 Numbers whose prime factorization exponents include at least one 1, at least one 3 and no other exponents.

24, 40, 54, 56, 88, 104, 120, 135, 136, 152, 168, 184, 189, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 344, 351, 375, 376, 378, 408, 424, 440, 456, 459, 472, 488, 513, 520, 536, 552, 568, 584, 594, 616, 621, 632, 664, 680, 686, 696, 702, 712, 728, 744, 750

Offset: 1

Author

Amiram Eldar, Jul 29 2024

Keywords

• nonn
• easy

Comments

First differs from its subsequence A360793 at n = 79: a(79) = 1080 = 2^3 * 3^3 * 5 is not a term of A360793.

Numbers k such that the set of distinct prime factorization exponents of k (row k of A136568) is {1, 3}.

The asymptotic density of this sequence is ((zeta(6)/zeta(3)) * Product_{p prime} (1 + 2/p^3 - 1/p^4 + 1/p^5) - 1)/zeta(2) = 0.076359822332835689478... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Equals A336591 \ (A005117 UNION A062838).

Subsequences: A065036, A360793.

Cf. A002117, A013661, A013664, A136568.

Programs

Mathematica

Select[Range[750], Union[FactorInteger[#][[;; , 2]]] == {1, 3} &]

PARI

is(k) = Set(factor(k)[,2]) == [1, 3];