A245729 Composite numbers n = A020639(n) * A032742(n) where the greatest proper divisor A032742(n) is greater than the square of the smallest prime factor A020639(n), and that greatest proper divisor A032742(n) is either a prime or satisfies the same condition (i.e., is itself the term of this sequence).

10, 14, 20, 22, 26, 28, 33, 34, 38, 39, 40, 44, 46, 51, 52, 56, 57, 58, 62, 66, 68, 69, 74, 76, 78, 80, 82, 86, 87, 88, 92, 93, 94, 99, 102, 104, 106, 111, 112, 114, 116, 117, 118, 122, 123, 124, 129, 132, 134, 136, 138, 141, 142, 145, 146, 148, 152, 153, 155, 156, 158, 159, 160, 164, 166, 171, 172, 174, 176, 177

Offset: 1

Author

Antti Karttunen and Reinhard Zumkeller, Jan 09 2015

Keywords

• nonn

Comments

If n is present, then so is also 2*n.

If n = p_1^e_1*p_2^e_2*... with p_1 > p_2 > ..., then n is in this sequence iff p_1^2 > p_2 and e_1 = 1. - Charlie Neder, Jun 13 2019

Examples

			10 = 2*5 is present, because 2^2 < 5 and 5 is a prime.
20 = 2*10 is present, because 2^2 < 10, and 10 itself is present in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A088381 and A251727.

Subsequences: A138511, A253569.

Cf. A001222, A000290, A010051, A020639, A032742.

Programs

Haskell

a245729 n = a245729_list !! (n-1)
a245729_list = filter f [1..] where
                      f x = p ^ 2 < q && (a010051' q == 1 || f q)
                            where q = div x p; p = a020639 x
-- Antti Karttunen after Reinhard Zumkeller's code for A138511, Jan 09 2015

Scheme

;; With Antti Karttunen's IntSeq-library.
(define (charfun_for_A245729 n) (if (and (> (A001222 n) 1) (> (A032742 n) (A000290 (A020639 n)))) (+ (A010051 (A032742 n)) (charfun_for_A245729 (A032742 n))) 0))
(define A245729 (NONZERO-POS 1 1 charfun_for_A245729))
;; Antti Karttunen, Jan 16 2015