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

1,1

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A131693 A255532 A307516 * A073492 A073493 A162685

Adjacent sequences: A069897 A069898 A069899 * A069901 A069902 A069903

Keyword

nonn,changed

Author

Labos Elemer, Apr 10 2002

Extensions

More terms from Reinhard Zumkeller, Mar 17 2003

Status

approved