A365866 Integers that are divisible by the cube of their least prime factor.

8, 16, 24, 27, 32, 40, 48, 56, 64, 72, 80, 81, 88, 96, 104, 112, 120, 125, 128, 135, 136, 144, 152, 160, 168, 176, 184, 189, 192, 200, 208, 216, 224, 232, 240, 243, 248, 256, 264, 272, 280, 288, 296, 297, 304, 312, 320, 328, 336, 343, 344, 351, 352, 360, 368, 376

Offset

1,1

Comments

Numbers k such that A067029(k) >= 3.

The asymptotic density of terms with least prime factor prime(n) (within all the positive integers) is d(n) = (1/(prime(n)^3) * Product_{k=1..(n-1)} (1-1/prime(k)). For example, for n = 1, 2, 3, 4, 5 and 6, d(n) = 1/8, 1/54, 1/375, 4/5145, 8/46585 and 16/169169.

The asymptotic density of this sequence is Sum_{n>=1} d(n) = 0.147333958520714364623977...

Links

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

Example

8 is a term since 2 is the least prime factor of 8 and 8 is divisible by 2^3 = 8.

Mathematica

Select[Range[400], FactorInteger[#][[1, -1]] >= 3 &]

Prog

(PARI) is(n) = n > 1 && factor(n)[1, 2] >= 3;

Crossrefs

Cf. A020639, A067029.

Subsequence of A046099 and A283050.

Subsequences: A365867, A365868.

Sequence in context: A046099 A344653 A345193 * A033859 A177899 A358727

Adjacent sequences: A365863 A365864 A365865 * A365867 A365868 A365869

Keyword

nonn,easy

Author

Amiram Eldar, Sep 21 2023

Status

approved