cp's OEIS Frontend

A101550 Lopsided (or biased) numbers: numbers n such that the largest prime factor of n is > 2*sqrt(n).

%I A101550 #50 Jul 09 2020 05:43:50
%S A101550 5,7,11,13,17,19,22,23,26,29,31,34,37,38,39,41,43,46,47,51,53,57,58,
%T A101550 59,61,62,67,68,69,71,73,74,76,79,82,83,86,87,89,92,93,94,97,101,103,
%U A101550 106,107,109,111,113,115,116,118,122,123,124,127,129,131,134,137,139,141
%N A101550 Lopsided (or biased) numbers: numbers n such that the largest prime factor of n is > 2*sqrt(n).
%C A101550 Note that all primes > 3 are here. See A101549 for composite lopsided numbers.
%C A101550 First differs from A320048 at a(51). - (After _R. J. Mathar_), - _Omar E. Pol_, Oct 04 2018
%C A101550 The asymptotic density of this sequence is log(2) (Chowla and Todd, 1949). - _Amiram Eldar_, Jul 09 2020
%H A101550 T. D. Noe, <a href="/A101550/b101550.txt">Table of n, a(n) for n = 1..1000</a>
%H A101550 S. D. Chowla and John Todd, <a href="https://doi.org/10.4153/CJM-1949-025-4">The Density of Reducible Integers</a>, Canadian Journal of Mathematics, Vol. 1, No. 3 (1949), pp. 297-299.
%H A101550 G. Everest, S. Stevens, D. Tamsett and T. Ward, <a href="https://arxiv.org/abs/math/0412079">Primitive Divisors of Quadratic Polynomial Sequences</a>, arXiv:math/0412079 [math.NT], 2004-2006.
%H A101550 G. Everest et al., <a href="http://www.jstor.org/stable/27642221">Primes generated by recurrence sequences</a>, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
%p A101550 with(numtheory): a:=proc(n) if max((seq(factorset(n)[j],j=1..nops(factorset(n)))))^2>4*n then n else fi end: seq(a(n),n=2..170); # _Emeric Deutsch_, May 27 2007
%t A101550 Select[Range[2, 200], FactorInteger[ # ][[ -1, 1]]>2Sqrt[ # ]&]
%Y A101550 Cf. A002162, A063763 (composite n such that the largest prime factor > sqrt(n)), A064052 (n such that the largest prime factor > sqrt(n)).
%K A101550 nonn
%O A101550 1,1
%A A101550 _T. D. Noe_, Dec 06 2004
%E A101550 Edited by _N. J. A. Sloane_, Jul 02 2008 at the suggestion of _R. J. Mathar_