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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

Equals A336591 \ (A005117 UNION A062838).

Subsequences: A065036, A360793.

Cf. A002117, A013661, A013664, A136568.

Sequence in context: A334801 A362594 A360793 * A297401 A065127 A065036

Adjacent sequences: A375073 A375074 A375075 * A375077 A375078 A375079

Keyword

nonn,easy

Author

Amiram Eldar, Jul 29 2024

Status

approved