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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 (list; graph; refs; listen; history; text; internal format)
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

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

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.

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

Sequence in context: A272374 A251727 A253785 * A031274 A272375 A246473

Adjacent sequences:  A245726 A245727 A245728 * A245730 A245731 A245732

KEYWORD

nonn

AUTHOR

Antti Karttunen and Reinhard Zumkeller, Jan 09 2015

STATUS

approved

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Last modified December 6 11:48 EST 2021. Contains 349563 sequences. (Running on oeis4.)