A069899 Numbers k such that the integer quotient of largest and smallest prime factors of k is 1.

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 23, 24, 25, 27, 29, 31, 32, 35, 36, 37, 41, 43, 45, 47, 48, 49, 53, 54, 59, 61, 64, 67, 71, 72, 73, 75, 77, 79, 81, 83, 89, 91, 96, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 135, 137, 139, 143, 144

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.

Numbers k > 1 such that A006530(k) < 2*A020639(k). - Amiram Eldar, Feb 10 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A081306(n+1). - Amiram Eldar, Feb 10 2025

Example

Beside primes and prime powers, composite numbers like 96 are terms because floor(3/2) = 1.

Mathematica

q[k_] := Module[{p = FactorInteger[k][[;; , 1]]}, p[[-1]] < 2*p[[1]]]; Select[Range[2, 150], q] (* Amiram Eldar, Feb 10 2025 *)

Prog

(PARI) isok(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, A069900, A081306.

Sequence in context: A193671 A073491 A066311 * A081306 A130073 A133812

Adjacent sequences: A069896 A069897 A069898 * A069900 A069901 A069902

Keyword

nonn,changed

Author

Labos Elemer, Apr 10 2002

Status

approved