A252374 a(n) = exponent k for the smallest r such that r^k <= spf(n) and gpf(n) < r^(k+1), for some k >= 0, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).

0, 1, 1, 1, 2, 1, 2, 1, 1, 0, 3, 1, 3, 0, 1, 1, 4, 1, 4, 0, 1, 0, 4, 1, 2, 0, 1, 0, 4, 0, 4, 1, 0, 0, 2, 1, 5, 0, 0, 0, 5, 0, 5, 0, 1, 0, 5, 1, 2, 0, 0, 0, 5, 1, 1, 0, 0, 0, 5, 0, 5, 0, 1, 1, 1, 0, 6, 0, 0, 0, 6, 1, 6, 0, 1, 0, 1, 0, 6, 0, 1, 0, 6, 0, 1, 0, 0, 0, 6, 0, 1, 0, 0, 0, 1, 1, 6, 0, 0, 0, 6, 0, 6, 0, 1, 0, 6, 1, 6, 0, 0, 0, 6, 0, 1, 0, 0, 0, 1, 0

Offset: 1

Author

Antti Karttunen, Dec 17 2014

Keywords

• nonn

Links

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

Crossrefs

Cf. A252375.

Cf. A251727 (gives the position of other zeros after a(1)=0).

Cf. also A006530, A020639, A066048.

Programs

Scheme

(define (A252374 n) (let ((spf (A020639 n)) (gpf (A006530 n))) (let outerloop ((r 2)) (let innerloop ((rx 1) (k 0)) (cond ((and (<= rx spf) (< gpf (* r rx))) k) ((<= rx spf) (innerloop (* r rx) (+ 1 k))) (else (outerloop (+ 1 r))))))))

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.]