%I #24 Sep 09 2017 19:28:02

%S 10,14,20,22,26,28,30,33,34,38,39,40,42,44,46,50,51,52,56,57,58,60,62,

%T 66,68,69,70,74,76,78,80,82,84,86,87,88,90,92,93,94,98,99,100,102,104,

%U 106,110,111,112,114,116,117,118,120,122,123,124,126,129,130,132,134,136,138,140,141,142,145,146,148,150,152

%N Numbers n > 1 for which gpf(n) > spf(n)^2, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).

%C Numbers n > 1 for which the smallest r such that r^k <= spf(n) and gpf(n) < r^(k+1) [for some k >= 0] is gpf(n)+1. Here spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n). (The original, equivalent definition of the sequence).

%C Numbers n > 1 such that A252375(n) = 1 + A006530(n). Equally, one can substitute A251725 for A252375.

%C Numbers n > 1 for which there doesn't exist any r <= gpf(n) such that r^k <= spf(n) and gpf(n) < r^(k+1), for some k >= 0, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).

%H Antti Karttunen, <a href="/A251727/b251727.txt">Table of n, a(n) for n = 1..10000</a>

%o (Scheme with _Antti Karttunen_'s IntSeq-library, three alternative versions)

%o (define A251727 (MATCHING-POS 1 2 (lambda (n) (> (A006530 n) (A000290 (A020639 n))))))

%o (define A251727 (MATCHING-POS 1 2 (lambda (n) (= (A251725 n) (+ 1 (A006530 n))))))

%o (define A251727 (MATCHING-POS 1 2 (lambda (n) (= (A252375 n) (+ 1 (A006530 n))))))

%Y Complement: A251726. Subsequence: A138511.

%Y Gives the positions of zeros in A252374 following its initial term.

%Y Cf. A252371 (difference between the prime indices of gpf and spf of each a(n)).

%Y Cf. A006530, A020639, A252375, A251725.

%Y Related permutations: A252757-A252758.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 17 2014. A new simpler definition found Jan 01 2015 and the original definition moved to the Comments section