cp's OEIS Frontend

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).

%I A245729 #31 Apr 01 2025 17:59:49
%S A245729 10,14,20,22,26,28,33,34,38,39,40,44,46,51,52,56,57,58,62,66,68,69,74,
%T A245729 76,78,80,82,86,87,88,92,93,94,99,102,104,106,111,112,114,116,117,118,
%U A245729 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
%N 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).
%C A245729 If n is present, then so is also 2*n.
%C A245729 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
%H A245729 Antti Karttunen, <a href="/A245729/b245729.txt">Table of n, a(n) for n = 1..10000</a>
%e A245729 10 = 2*5 is present, because 2^2 < 5 and 5 is a prime.
%e A245729 20 = 2*10 is present, because 2^2 < 10, and 10 itself is present in the sequence.
%o A245729 (Haskell)
%o A245729 a245729 n = a245729_list !! (n-1)
%o A245729 a245729_list = filter f [1..] where
%o A245729                       f x = p ^ 2 < q && (a010051' q == 1 || f q)
%o A245729                             where q = div x p; p = a020639 x
%o A245729 -- _Antti Karttunen_ after _Reinhard Zumkeller_'s code for A138511, Jan 09 2015
%o A245729 (Scheme)
%o A245729 ;; With Antti Karttunen's IntSeq-library.
%o A245729 (define (charfun_for_A245729 n) (if (and (> (A001222 n) 1) (> (A032742 n) (A000290 (A020639 n)))) (+ (A010051 (A032742 n)) (charfun_for_A245729 (A032742 n))) 0))
%o A245729 (define A245729 (NONZERO-POS 1 1 charfun_for_A245729))
%o A245729 ;; _Antti Karttunen_, Jan 16 2015
%Y A245729 Subsequence of A088381 and A251727.
%Y A245729 Subsequences: A138511, A253569.
%Y A245729 Cf. A001222, A000290, A010051, A020639, A032742.
%K A245729 nonn
%O A245729 1,1
%A A245729 _Antti Karttunen_ and _Reinhard Zumkeller_, Jan 09 2015