login
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).
4
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
1,1
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
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
Subsequence of A088381 and A251727.
Subsequences: A138511, A253569.
Sequence in context: A362982 A251727 A253785 * A031274 A272375 A246473
KEYWORD
nonn
AUTHOR
STATUS
approved