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%I #9 Jan 16 2015 18:22:49
%S 10,14,20,22,26,28,33,34,38,39,40,44,46,50,51,52,56,57,58,62,66,68,69,
%T 70,74,76,78,80,82,86,87,88,92,93,94,98,99,100,102,104,106,110,111,
%U 112,114,116,117,118,122,123,124,129,130,132,134,136,138,140,141,142,145,146,148,152,153,154,155,156,158,159,160,164,166,170
%N Composite numbers n = prime(i_1) * ... * prime(i_k), prime(i_1) <= prime(i_2) <= ... <= prime(i_k), with at least one pair of successive prime factors (when sorted into monotonic order) where the latter prime factor is greater than the square of the former: prime(i_x)^2 < prime(i_{x+1}), for some x in 1 .. k-1, where k = A001222(n) and i_k = A061395(n).
%H Antti Karttunen, <a href="/A253785/b253785.txt">Table of n, a(n) for n = 1..10000</a>
%e 10 = 2*5 is present as 2^2 < 5.
%e 50 = 2*5*5 is present as 2^2 < 5.
%e 51 = 3*17 is present as 3^2 < 17.
%e 66 = 2*3*11 is present as 3^2 < 11.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A253785 (MATCHING-POS 1 1 (lambda (n) (not (numbers-densely-distributed? (ifactor n))))))
%o (define (numbers-densely-distributed? lista) (cond ((null? lista) #t) ((null? (cdr lista)) #t) ((< (A000290 (car lista)) (cadr lista)) #f) (else (numbers-densely-distributed? (cdr lista)))))
%Y Complement: A253784.
%Y Subsequences: A138511, A253569.
%Y Cf. A000290, A001222, A061395.
%Y Differs from A245729 for the first time at n=14, where a(14) = 50, while A245729(14) = 51.
%K nonn
%O 1,1
%A _Antti Karttunen_, Jan 16 2015
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