|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|