%I #33 Jan 12 2024 10:04:31
%S 98,475,548,603,724,844,845,1274,1420,1681,1682,1924,2275,2523,2890,
%T 3283,3474,3548,3626,3716,4148,4203,4418,4475,4850,4923,4948,5202,
%U 5274,5490,5524,5634,5948,6650,6811,6956,7299,7324,7442,7514,7675,8107,8348
%N First of 3 consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2} are in A067259.
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 1, 7, 55, 570, 5628, 56174, 562151, 5621119, 56209006, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00562... . - _Amiram Eldar_, Jan 18 2023
%C The asymptotic density of this sequence is Product_{p prime} (1 - 3/p^3) - 3 * Product_{p prime} (1 - 1/p^2 - 2/p^3) + 3 * Product_{p prime} (1 - 2/p^2 - 1/p^3) - Product_{p prime} (1 - 3/p^2) = 0.0056209097169531390208... . - _Amiram Eldar_, Jan 12 2024
%H Michael De Vlieger, <a href="/A071319/b071319.txt">Table of n, a(n) for n = 1..10000</a>
%F A051903(k) = A051903(k+1) = A051903(k+2) = 2 when k is a term.
%e 98 is a term since 98 = 2*7^2, 99 = 3^2*11, and 100 = 2^2*5^2.
%t With[{s = Select[Range[10^4], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ SequencePosition[t, {1, 1}][[All, 1]]]@ Differences@ s] (* _Michael De Vlieger_, Jul 30 2017 *)
%o (PARI) isok(n) = (n>1) && (vecmax(factor(n)[, 2])==2) && (vecmax(factor(n+1)[, 2])==2) && (vecmax(factor(n+2)[, 2])==2); \\ _Michel Marcus_, Aug 02 2017
%Y Subsequence of A067259 and A071318.
%Y Cf. A051903, A063528.
%K nonn
%O 1,1
%A _Labos Elemer_, May 29 2002