A144775 - OEIS

%I #3 Mar 31 2012 10:28:53

%S 0,1,2,0,4,0,6,3,2,0,10,0,12,0,0,4,16,8,18,0,0,0,22,13,7,0,2,0,28,0,

%T 30,5,0,0,0,16,36,0,0,24,40,0,42,0,21,0,46,16,13,15,0,0,52,11,0,35,0,

%U 0,58,0,60,0,31,5,0,0,66,0,0,0,70,20,72,0,27,0,0,0,78,32,2,0,82,0,0,0,0,55

%N Define f(n) = 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 This sequence obtains a new maximum a(n) = n - 1 for prime n.

%C a(n) = 0 often, but not always, when n - 1 and n + 1 are twin primes.

%e f(8) = 2 * rad(8) = 4. f(k) < 4 for 1, 2 and 3 (f(k) = k for 0 < k < 8); a(8) = 3.

%Y Cf. A000040, A001097, A007947, A144100, A144774

%K easy,nonn

%O 1,3

%A _Reikku Kulon_, Sep 21 2008