|
%I #11 Dec 30 2020 03:35:17
%S 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,
%T 36,37,38,41,42,43,44,45,46,49,50,51,52,57,58,59,60,61,62,65,66,67,68,
%U 69,70,73,74,75,76,77,78,82,83,84,85,86,89,90,91,92,93,94
%N Numbers k such that k and k+1 are both cubefree numbers (A004709).
%C The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^3) = 0.6768927370... (A340153) (Carlitz, 1932).
%H Amiram Eldar, <a href="/A340152/b340152.txt">Table of n, a(n) for n = 1..10000</a>
%H Leonard Carlitz, <a href="https://doi.org/10.1093/qmath/os-3.1.273">On a problem in additive arithmetic (II)</a>, The Quarterly Journal of Mathematics, Vol. os-3, No. 1 (1932), pp. 273-290.
%e 1 is a term since both 1 and 2 are cubefree numbers.
%e 7 is not a term since 7+1 = 8 = 2^3 is not cubefree.
%t cubefreeQ[n_] := Max @ FactorInteger[n][[;; , 2]] < 3; Select[Range[100], cubefreeQ[#] && cubefreeQ[# + 1] &]
%Y Subsequence of A004709.
%Y Subsequences: A007674, A328016.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Dec 29 2020
|
