OFFSET
1,2
COMMENTS
In other words, {1} together with primes and such composite numbers n = p_i * p_j * p_k * ... * p_u, p_i <= p_j <= p_k <= ... <= p_u, where each successive prime factor (when sorted into a nondecreasing order) is less than the square of the previous: (p_i)^2 > p_j, (p_j)^2 > p_k, etc.
Whenever gcd(a(i),a(j)) > 1, then a(i)*a(j) and lcm(a(i),a(j)) are also members of this sequence.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
EXAMPLE
1 is present as it has an empty prime factorization.
2 like all primes is present.
4 = 2*2 is present as 2^2 > 2.
9 = 3*3 is present as 3^2 > 3.
10 = 2*5 is NOT present, as 2^2 < 5.
30 = 2*3*5 is present, as 2^2 > 3 and 3^2 > 5.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A253784 (MATCHING-POS 1 1 (lambda (n) (numbers-densely-distributed? (ifactor n)))))
(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)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 16 2015
STATUS
approved