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

1,1

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.

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[ # ]&]

Crossrefs

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

Sequence in context: A113909 A111906 A348471 * A320048 A246351 A272260

Adjacent sequences: A101547 A101548 A101549 * A101551 A101552 A101553

Keyword

nonn

Author

T. D. Noe, Dec 06 2004

Extensions

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

Status

approved