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A144776 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).

%I A144776 #7 Jul 03 2018 16:57:01
%S A144776 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,
%T A144776 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,
%U A144776 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
%N A144776 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).
%C A144776 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.
%H A144776 Antti Karttunen, <a href="/A144776/b144776.txt">Table of n, a(n) for n = 1..65537</a>
%e A144776 f(8) = 4 and f(9) = 3. For 1, 2, 3, 5 and 7, f(k) = 1, so a(8) = a(9) = 5.
%o A144776 (PARI)
%o A144776 A007947(n) = factorback(factorint(n)[, 1]);
%o A144776 f(n) = if(isprime(n),1,if(n%4,A007947(n),2*A007947(n)));
%o A144776 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
%Y A144776 Cf. A000040, A001097, A007947, A144100, A144774, A144775
%K A144776 easy,nonn
%O A144776 1,8
%A A144776 _Reikku Kulon_, Sep 21 2008