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 A251726 Numbers n > 1 for which gpf(n) < lpf(n)^2, where lpf and gpf (least and greatest prime factor of n) are given by A020639(n) and A006530(n). 17
 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 21, 23, 24, 25, 27, 29, 31, 32, 35, 36, 37, 41, 43, 45, 47, 48, 49, 53, 54, 55, 59, 61, 63, 64, 65, 67, 71, 72, 73, 75, 77, 79, 81, 83, 85, 89, 91, 95, 96, 97, 101, 103, 105, 107, 108, 109, 113, 115, 119, 121, 125, 127, 128, 131, 133, 135, 137, 139, 143, 144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n > 1 for which there exists r <= gpf(n) such that r^k <= lpf(n) and gpf(n) < r^(k+1) for some k >= 0, where lpf and gpf (least and greatest prime factor of n) are given by A020639(n) and A006530(n) (the original, equivalent definition of the sequence). Numbers n > 1 such that A252375(n) < 1 + A006530(n). Equally, one can substitute A251725 for A252375. These are numbers n all of whose prime factors "fit between" two consecutive powers of some positive integer which itself is <= the largest prime factor of n. Conjecture: If any n is in the sequence, then so is A003961(n). Note: if Legendre's or Brocard's conjecture is true, then the above conjecture is true as well. See my comments at A251728. - Antti Karttunen, Jan 01 2015 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Ratio A251726(n)/A251727(n) (plotted with OEIS-server's Plot2-utility) FORMULA Other identities. For all n >= 1: A252373(a(n)) = n. [A252373 works as an inverse or ranking function for this sequence.] EXAMPLE For 35 = 5*7, 7 is less than 5^2, thus 35 is included. For 90 = 2*3*3*5, 5 is not less than 2^2, thus 90 is NOT included. For 105 = 3*5*7, 7 is less than 3^2, thus 105 is included. MATHEMATICA pfQ[n_]:=Module[{f=FactorInteger[n]}, f[[-1, 1]] 1 for which A284252(n) (equally: A284254) is 1, and A284256(n) (equally A284258) is 0, and also n > 1 such that A284260(n) = A006530(n). Cf. A003961, A006530, A020639, A252375, A251725, A253784. Related permutations: A252757-A252758. Sequence in context: A253567 A048197 A253784 * A193671 A073491 A066311 Adjacent sequences:  A251723 A251724 A251725 * A251727 A251728 A251729 KEYWORD nonn AUTHOR Antti Karttunen, Dec 17 2014 EXTENSIONS A new simpler definition found Jan 01 2015 and the original definition moved to the Comments section. STATUS approved

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Last modified May 19 10:50 EDT 2019. Contains 323390 sequences. (Running on oeis4.)