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A340152
Numbers k such that k and k+1 are both cubefree numbers (A004709).
12
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
1,2
COMMENTS
The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^3) = 0.6768927370... (A340153) (Carlitz, 1932).
LINKS
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: A354047 A031487 A047422 * A160532 A047305 A032878
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 29 2020
STATUS
approved