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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). 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 05:52 EST 2021. Contains 340333 sequences. (Running on oeis4.)