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%I #30 Jan 18 2023 03:25:03
%S 844,1681,8523,8954,10050,10924,11322,17404,19940,22020,23762,24450,
%T 25772,27547,30923,30924,33172,34347,38724,39050,39347,40050,47673,
%U 47724,47825,49147,54585,55449,57474,58473,58849,58867,59924,62865
%N Least of four consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2, k+3} are in A067259.
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 0, 1, 4, 57, 555, 5492, 55078, 551443, 5512825, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000551... . - _Amiram Eldar_, Jan 18 2023
%H Amiram Eldar, <a href="/A071320/b071320.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Michael De Vlieger)
%F A051903(k) = A051903(k+1) = A051903(k+2) = A051903(k+3) = 2 when k is a term.
%e k = 844 is a term since 844 = 2^2*211, k+1 = 845 = 5*13^2, k+2 = 846 = 2*3^2*47, and k+4 = 847 = 7*11^2.
%t With[{s = Select[Range[10^5], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ SequencePosition[t, {1, 1, 1}][[All, 1]]]@ Differences@ s] (* _Michael De Vlieger_, Jul 30 2017 *)
%Y Subsequence of A067259, A071318 and A071319.
%Y Cf. A051903, A063528.
%K nonn
%O 1,1
%A _Labos Elemer_, May 29 2002
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