A252372 Characteristic function for A251726: a(n) = 1 if n > 1 and gpf(n) < spf(n)^2, otherwise 0; here spf(n) and gpf(n) (smallest and greatest prime factor of n) are sequences A020639(n) and A006530(n).

0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0

Offset

1

Comments

a(n) = 1 if n > 1 and there exists r <= A006530(n) such that r^k <= A020639(n) and A006530(n) < r^(k+1) for some k >= 0, otherwise 0 (the original definition).

Links

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

Formula

Other identities. For all n >= 1:

a(n) = a(A066048(n)). [The result depends only on the smallest and the largest prime factor of n.]

Prog

(Scheme) (define (A252372 n) (if (< (A252375 n) (+ 1 (A006530 n))) 1 0))

Crossrefs

Characteristic function of A251726.

A252373 gives the partial sums.

Cf. A006530, A020639, A066048, A252459, A252757.

Sequence in context: A368916 A324732 A164980 * A168182 A204447 A368905

Adjacent sequences: A252369 A252370 A252371 * A252373 A252374 A252375

Keyword

nonn

Author

Antti Karttunen, Dec 17 2014. A new simpler definition found Jan 04 2015 and the original definition moved to the Comments section.

Status

approved