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

1,1

Links

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

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.]

Prog

(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.

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.

Sequence in context: A126696 A244464 A250201 * A339170 A257773 A164898

Adjacent sequences: A252372 A252373 A252374 * A252376 A252377 A252378

Keyword

nonn

Author

Antti Karttunen, Dec 17 2014

Status

approved