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

Author

Amiram Eldar, Sep 21 2023

Keywords

• nonn
• easy

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...

Examples

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

Links

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

Crossrefs

Cf. A020639, A067029.

Subsequence of A046099 and A283050.

Subsequences: A365867, A365868.

Programs

Mathematica

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

PARI

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