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 A345896 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). 1
 2673, 10625, 12168, 14651, 24167, 28800, 32085, 34162, 48279, 50692, 59892, 60928, 61347, 61952, 64960, 66125, 66339, 70400, 71995, 74704, 80730, 83028, 89424, 93024, 96348, 100491, 108675, 111475, 112632, 114954, 117649, 118048, 121121, 122877, 127224, 144925, 147204, 149178, 150072, 153340 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MathOverflow, Can all three numbers n, n^2-1, n^2+1 be fine (as opposed to coarse)? EXAMPLE a(3) = 12168 is a term because: A006530(12168) = 13 with 13^3 = 2197 < 12168, 12168^2-1 = 148060223, A006530(148060223) = 283 with 283^3 = 22665187 < 148060223, and 12168^2+1 = 148060225, A006530(148060225) = 293 with 293^3 = 25153757 < 148060225. MAPLE isfine:= proc(n) andmap(t -> t^3 < n, numtheory:-factorset(n)) end proc: filter:= t -> isfine(t) and isfine(t^2-1) and isfine(t^2+1): select(filter, [\$1..200000]); CROSSREFS Cf. A006530. Sequence in context: A235253 A309762 A344192 * A085559 A123075 A112138 Adjacent sequences: A345893 A345894 A345895 * A345897 A345898 A345899 KEYWORD nonn AUTHOR Robert Israel, Jun 29 2021 STATUS approved

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Last modified August 5 17:52 EDT 2024. Contains 374954 sequences. (Running on oeis4.)