A069900 Numbers k such that the integer quotient of largest and smallest prime factors of k is greater than one.

10, 14, 20, 21, 22, 26, 28, 30, 33, 34, 38, 39, 40, 42, 44, 46, 50, 51, 52, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 76, 78, 80, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 98, 99, 100, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120

Offset: 1

Author

Labos Elemer, Apr 10 2002

Keywords

• nonn

Comments

Numbers k such that A069897(k) = floor(P(k)/p(k)) > 1, where P(k) and p(k) are largest and least prime factor of k, respectively.

Also numbers having at least one prime factor greater than twice the smallest prime factor: complement of A081306. - Reinhard Zumkeller, Mar 17 2003

Examples

			Composites with at least two and sufficiently deviating prime factors are here, like 2q, where q = prime >= 5: {10, ..., 254}.
Numbers with such divisors like 30 are also included.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A020639, A069897, A069899, A081303, A081306.

Programs

Mathematica

Select[Range@ 120, #[[-1]] > 2 #[[1]] &@ FactorInteger[#][[All, 1]] &] (* Michael De Vlieger, Dec 08 2018 *)

PARI

is(k) = if(k == 1, 0, my(p = factor(k)[,1]); p[#p] > 2*p[1]); \\ Amiram Eldar, Feb 10 2025

Formula

A081303(a(n)) > 0. - Reinhard Zumkeller, Mar 17 2003

Extensions

More terms from Reinhard Zumkeller, Mar 17 2003