A386800 Numbers that have exactly one exponent in their prime factorization that is equal to 3.

8, 24, 27, 40, 54, 56, 72, 88, 104, 108, 120, 125, 135, 136, 152, 168, 184, 189, 200, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 360, 375, 376, 378, 392, 408, 424, 432, 440, 456, 459, 472, 488, 500, 504, 513, 520, 536, 540, 552, 568, 584

Offset

1,1

Comments

First differs from its subsequence A381315 at n = 40: a(40) = 432 = 2^4 * 3^3 is not a term of A381315.

Numbers k such that A295883(k) = 1.

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^3 + 1/p^4) * Sum_{p prime} (p-1)/(p^4 - p + 1) = 0.092831691827595439609... (Elma and Martin, 2024).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Ertan Elma and Greg Martin, Distribution of the number of prime factors with a given multiplicity, Canadian Mathematical Bulletin, Vol. 67, No. 4 (2024), pp. 1107-1122; arXiv preprint, arXiv:2406.04574 [math.NT], 2024.

Index entries for sequences computed from indices in prime factorization.

Mathematica

f[p_, e_] := If[e == 3, 1, 0]; s[1] = 0; s[n_] := Plus @@ f @@@ FactorInteger[n]; Select[Range[300], s[#] == 1 &]

Prog

(PARI) isok(k) = vecsum(apply(x -> if(x == 3, 1, 0), factor(k)[, 2])) == 1;

Crossrefs

A381315 is subsequence.

Cf. A295883.

Numbers that have exactly one exponent in their prime factorization that is equal to k: A119251 (k=1), A386796 (k=2), this sequence (k=3), A386804 (k=4), A386808 (k=5).

Numbers that have exactly m exponents in their prime factorization that are equal to 3: A386799 (m=0), this sequence (m=1), A386801 (m=2), A386802 (m=3).

Sequence in context: A336593 A176297 A375072 * A381315 A175496 A048109

Adjacent sequences: A386797 A386798 A386799 * A386801 A386802 A386803

Keyword

nonn,easy

Author

Amiram Eldar, Aug 03 2025

Status

approved