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
Michael De Vlieger, Table of n, a(n) for n = 1..10000
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
Labos Elemer, May 29 2002
STATUS
approved