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%I #12 Jul 01 2021 15:52:44
%S 2673,10625,12168,14651,24167,28800,32085,34162,48279,50692,59892,
%T 60928,61347,61952,64960,66125,66339,70400,71995,74704,80730,83028,
%U 89424,93024,96348,100491,108675,111475,112632,114954,117649,118048,121121,122877,127224,144925,147204,149178,150072,153340
%N Numbers k such that k, k^2-1 and k^2+1 are all fine, where a number m is fine if its prime factors are all less than m^(1/3).
%C Numbers k such that A006530(k)^3 < k, A006530(k^2-1)^3 < k^2-1, and A006530(k^2+1)^3 < k^2+1.
%H Robert Israel, <a href="/A345896/b345896.txt">Table of n, a(n) for n = 1..10000</a>
%H MathOverflow, <a href="https://mathoverflow.net/questions/396310/can-all-three-numbers-n-n2-1-n21-be-fine-as-opposed-to-coarse/396318#comment1014828_396318">Can all three numbers n, n^2-1, n^2+1 be fine (as opposed to coarse)?</a>
%e a(3) = 12168 is a term because:
%e A006530(12168) = 13 with 13^3 = 2197 < 12168,
%e 12168^2-1 = 148060223, A006530(148060223) = 283 with 283^3 = 22665187 < 148060223, and
%e 12168^2+1 = 148060225, A006530(148060225) = 293 with 293^3 = 25153757 < 148060225.
%p isfine:= proc(n) andmap(t -> t^3 < n, numtheory:-factorset(n)) end proc:
%p filter:= t -> isfine(t) and isfine(t^2-1) and isfine(t^2+1):
%p select(filter, [$1..200000]);
%Y Cf. A006530.
%K nonn
%O 1,1
%A _Robert Israel_, Jun 29 2021
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