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.

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, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 56, 59, 60, 61, 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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

4 = 2*2 is present as 2^2 > 2.
6 = 2*3 is present as 2^2 > 3.
70 = 2*5*7 is present as 5^2 > 7.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A253567 (MATCHING-POS 1 1 (lambda (n) (or (< (A001222 n) 2) (not (numbers-sparsely-distributed? (ifactor n)))))))
(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)))))

Crossrefs

Complement: A253569.

Subsequences: A008578, A013929, A251728, A253784.

Cf. A001222.

Sequence in context: A305933 A105208 A074779 * A048197 A253784 A342191

Adjacent sequences: A253564 A253565 A253566 * A253568 A253569 A253570

Keyword

nonn

Author

Antti Karttunen, Jan 16 2015

Status

approved