A330729 Numbers k that are divisible by all integers less than or equal to the cube root of k.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 36, 42, 48, 54, 60, 72, 84, 96, 108, 120, 180, 240, 300, 420

Offset: 1

Author

Eric Fox, Dec 28 2019

Keywords

• nonn
• fini
• full

Examples

			42 appears because the cube root of 42 is approximately 3.48 and 42 is divisible by 3, 2, and 1 (all positive integers less than 3.48).
		

Crossrefs

Cf. A003102.

Programs

Magma

[k: k in [1..500]|forall{m:m in [1..Floor(k^(1/3))]|k mod m eq 0}]; // Marius A. Burtea, Dec 31 2019

Mathematica

Select[Range[1000], Divisible[#, LCM @@ Range @ Floor @ Surd[#, 3]] &] (* Amiram Eldar, Dec 28 2019 *)

PARI

is(k) = {my(m=sqrtnint(k, 3)); sum(i=1, m, Mod(k, i)==0) == m; } \\ Jinyuan Wang, Dec 31 2019