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A144776
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Define f(n) = 1 if n is prime, 2 * rad(n) if four divides n and rad(n) otherwise: then a(n) = 0 for composite n where f(n) is not less than n and otherwise equals the number of positive integers k less than n for which f(k) < f(n).
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1
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0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 8, 0, 12, 0, 0, 0, 0, 0, 17, 14, 0, 10, 0, 0, 0, 0, 14, 0, 0, 0, 22, 0, 0, 0, 28, 0, 0, 0, 0, 29, 0, 0, 26, 25, 26, 0, 0, 0, 24, 0, 42, 0, 0, 0, 0, 0, 0, 41, 21, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 42, 0, 0, 0, 0, 46, 23, 0, 0, 0, 0, 0, 0, 64, 0, 58, 0, 0, 0, 0, 0
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OFFSET
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1,8
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COMMENTS
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For the given terms, nearly all n for which a(n) obtains a new maximum are multiples of eight. Only 18, 36 and 45 are not.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
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EXAMPLE
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f(8) = 4 and f(9) = 3. For 1, 2, 3, 5 and 7, f(k) = 1, so a(8) = a(9) = 5.
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PROG
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(PARI)
A007947(n) = factorback(factorint(n)[, 1]);
f(n) = if(isprime(n), 1, if(n%4, A007947(n), 2*A007947(n)));
A144776(n) = if(n<2, 0, my(x=f(n)); if(!isprime(n)&&(x>=n), 0, sum(k=1, n-1, (f(k)<x)))); \\ Antti Karttunen, Jul 03 2018
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CROSSREFS
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Cf. A000040, A001097, A007947, A144100, A144774, A144775
Sequence in context: A186639 A266668 A043299 * A065937 A197738 A189232
Adjacent sequences: A144773 A144774 A144775 * A144777 A144778 A144779
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KEYWORD
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easy,nonn
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AUTHOR
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Reikku Kulon, Sep 21 2008
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STATUS
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approved
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