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

5, 7, 11, 13, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 67, 68, 69, 71, 73, 74, 76, 79, 82, 83, 86, 87, 89, 92, 93, 94, 97, 101, 103, 106, 107, 109, 111, 113, 115, 116, 118, 122, 123, 124, 127, 129, 131, 134, 137, 139, 141

Offset: 1

Author

T. D. Noe, Dec 06 2004

Keywords

• nonn

Comments

Note that all primes > 3 are here. See A101549 for composite lopsided numbers.

First differs from A320048 at a(51). - (After R. J. Mathar), - Omar E. Pol, Oct 04 2018

The asymptotic density of this sequence is log(2) (Chowla and Todd, 1949). - Amiram Eldar, Jul 09 2020

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• S. D. Chowla and John Todd, The Density of Reducible Integers, Canadian Journal of Mathematics, Vol. 1, No. 3 (1949), pp. 297-299.
• G. Everest, S. Stevens, D. Tamsett and T. Ward, Primitive Divisors of Quadratic Polynomial Sequences, arXiv:math/0412079 [math.NT], 2004-2006.
• G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

Crossrefs

Cf. A002162, A063763 (composite n such that the largest prime factor > sqrt(n)), A064052 (n such that the largest prime factor > sqrt(n)).

Programs

Maple

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

Mathematica

Select[Range[2, 200], FactorInteger[ # ][[ -1, 1]]>2Sqrt[ # ]&]

Extensions

Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar