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A071319
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.
3
98, 475, 548, 603, 724, 844, 845, 1274, 1420, 1681, 1682, 1924, 2275, 2523, 2890, 3283, 3474, 3548, 3626, 3716, 4148, 4203, 4418, 4475, 4850, 4923, 4948, 5202, 5274, 5490, 5524, 5634, 5948, 6650, 6811, 6956, 7299, 7324, 7442, 7514, 7675, 8107, 8348
OFFSET
1,1
COMMENTS
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
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
LINKS
FORMULA
A051903(k) = A051903(k+1) = A051903(k+2) = 2 when k is a term.
EXAMPLE
98 is a term since 98 = 2*7^2, 99 = 3^2*11, and 100 = 2^2*5^2.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Subsequence of A067259 and A071318.
Sequence in context: A306214 A160828 A158129 * A263040 A263033 A239173
KEYWORD
nonn
AUTHOR
Labos Elemer, May 29 2002
STATUS
approved