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A340152 Numbers k such that k and k+1 are both cubefree numbers (A004709). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Subsequence of A004709.

Subsequences: A007674, A328016.

Sequence in context: A037475 A031487 A047422 * A160532 A047305 A032878

Adjacent sequences:  A340149 A340150 A340151 * A340153 A340154 A340155

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Dec 29 2020

STATUS

approved

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Last modified April 10 22:21 EDT 2021. Contains 342856 sequences. (Running on oeis4.)