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A071320
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.
2
844, 1681, 8523, 8954, 10050, 10924, 11322, 17404, 19940, 22020, 23762, 24450, 25772, 27547, 30923, 30924, 33172, 34347, 38724, 39050, 39347, 40050, 47673, 47724, 47825, 49147, 54585, 55449, 57474, 58473, 58849, 58867, 59924, 62865
OFFSET
1,1
COMMENTS
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Michael De Vlieger)
FORMULA
A051903(k) = A051903(k+1) = A051903(k+2) = A051903(k+3) = 2 when k is a term.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Subsequence of A067259, A071318 and A071319.
Sequence in context: A038013 A334183 A078144 * A338628 A323253 A160212
KEYWORD
nonn
AUTHOR
Labos Elemer, May 29 2002
STATUS
approved