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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).
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%I #9 Dec 18 2014 02:07:27

%S 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,

%T 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,

%U 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

%N 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).

%H Antti Karttunen, <a href="/A252374/b252374.txt">Table of n, a(n) for n = 1..10000</a>

%F Other identities. For all n >= 1:

%F a(n) = a(A066048(n)). [The result depends only on the smallest and the largest prime factor of n.]

%o (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))))))))

%Y Cf. A252375.

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

%Y Cf. also A006530, A020639, A066048.

%K nonn

%O 1,5

%A _Antti Karttunen_, Dec 17 2014