cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A253567 Noncomposites together with such composites n = p_i * p_j * p_k * ... * p_u, p_i <= p_j <= p_k <= ... <= p_u, where there is at least one such pair of successive prime factors (when sorted into a nondecreasing order) that the square of the former is larger than the latter: (p_i)^2 > p_j or (p_j)^2 > p_k, etc.

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%I A253567 #15 Dec 28 2015 02:04:18
%S A253567 1,2,3,4,5,6,7,8,9,11,12,13,15,16,17,18,19,20,21,23,24,25,27,28,29,30,
%T A253567 31,32,35,36,37,40,41,42,43,44,45,47,48,49,50,52,53,54,55,56,59,60,61,
%U A253567 63,64,65,66,67,68,70,71,72,73,75,76,77,78,79,80,81,83,84,85,88,89,90,91,92,95,96,97,98,99,100
%N A253567 Noncomposites together with such composites n = p_i * p_j * p_k * ... * p_u, p_i <= p_j <= p_k <= ... <= p_u, where there is at least one such pair of successive prime factors (when sorted into a nondecreasing order) that the square of the former is larger than the latter: (p_i)^2 > p_j or (p_j)^2 > p_k, etc.
%H A253567 Antti Karttunen, <a href="/A253567/b253567.txt">Table of n, a(n) for n = 1..10000</a>
%e A253567 4 = 2*2 is present as 2^2 > 2.
%e A253567 6 = 2*3 is present as 2^2 > 3.
%e A253567 70 = 2*5*7 is present as 5^2 > 7.
%o A253567 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A253567 (define A253567 (MATCHING-POS 1 1 (lambda (n) (or (< (A001222 n) 2) (not (numbers-sparsely-distributed? (ifactor n)))))))
%o A253567 (define (numbers-sparsely-distributed? lista) (cond ((null? lista) #t) ((null? (cdr lista)) #t) ((> (A000290 (car lista)) (cadr lista)) #f) (else (numbers-sparsely-distributed? (cdr lista)))))
%Y A253567 Complement: A253569.
%Y A253567 Subsequences: A008578, A013929, A251728, A253784.
%Y A253567 Cf. A001222.
%K A253567 nonn
%O A253567 1,2
%A A253567 _Antti Karttunen_, Jan 16 2015