A252375 a(n) = 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).

2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 8, 3, 2, 2, 2, 2, 6, 3, 12, 2, 2, 2, 14, 2, 8, 2, 6, 2, 2, 12, 18, 2, 2, 2, 20, 14, 6, 2, 8, 2, 12, 3, 24, 2, 2, 2, 6, 18, 14, 2, 2, 4, 8, 20, 30, 2, 6, 2, 32, 3, 2, 4, 12, 2, 18, 24, 8, 2, 2, 2, 38, 3, 20, 4, 14, 2, 6, 2, 42, 2, 8, 5, 44, 30, 12, 2, 6, 4, 24, 32

Offset: 1

Author

Antti Karttunen, Dec 17 2014

Keywords

• nonn

Links

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

Crossrefs

A252374 gives the corresponding exponents.

Cf. A251726 (those n for which a(n) <= A006530(n)).

Cf. A251727 (those n > 1 for which a(n) = A006530(n)+1).

Cf. A006530, A020639, A066048, A138510, A251725.

Programs

Scheme

(define (A252375 n) (let ((spf (A020639 n)) (gpf (A006530 n))) (let outerloop ((r 2)) (let innerloop ((rx 1)) (cond ((and (<= rx spf) (< gpf (* r rx))) r) ((<= rx spf) (innerloop (* r rx))) (else (outerloop (+ 1 r))))))))
(define (A252375 n) (let ((x (A251725 n))) (if (= 1 x) 2 x))) ;; Alternatively, using the implementation of A251725.

Formula

If A251725(n) = 1, a(n) = 2, otherwise a(n) = A251725(n).

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.]