A340152 Numbers k such that k and k+1 are both cubefree numbers (A004709).

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 28, 29, 30, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94

Offset: 1

Author

Amiram Eldar, Dec 29 2020

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^3) = 0.6768927370... (A340153) (Carlitz, 1932).

Examples

			1 is a term since both 1 and 2 are cubefree numbers.
7 is not a term since 7+1 = 8 = 2^3 is not cubefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Leonard Carlitz, On a problem in additive arithmetic (II), The Quarterly Journal of Mathematics, Vol. os-3, No. 1 (1932), pp. 273-290.

Crossrefs

Subsequence of A004709.

Subsequences: A007674, A328016.

Programs

Mathematica

cubefreeQ[n_] := Max @ FactorInteger[n][[;; , 2]] < 3; Select[Range[100], cubefreeQ[#] && cubefreeQ[# + 1] &]