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

1,5

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 (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))))))))

Crossrefs

Cf. A252375.

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

Cf. also A006530, A020639, A066048.

Sequence in context: A029443 A078508 A029416 * A344569 A341094 A346831

Adjacent sequences: A252371 A252372 A252373 * A252375 A252376 A252377

Keyword

nonn

Author

Antti Karttunen, Dec 17 2014

Status

approved