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%I #8 Sep 16 2015 13:41:28
%S 1,1,1,2,3,1,3,1,1,2,6,1,1,2,4,1,1,1,3,1,1,2,3,1,2,3,2,1,4,6,1,3,1,3,
%T 2,8,3,2,3,3,1,2,6,2,1,3,3,1,5,4,3,2,1,3,1,4,2,1,3,2,1,3,1,1,3,1,1,2,
%U 6,2,4,5,3,1,3,2,1,3,3,1,3
%N a(n) is the smallest positive integer such that the numerator of (Sum_{k=1..n} 1/a(k)) is prime (or 1), for all positive integers n.
%e The sum of the reciprocals of the first 9 terms is 1 + 1 + 1 + 1/2 + 1/3 + 1 + 1/3 + 1 + 1 = 43/6. (And the numerator, 43, is prime.) Adding the reciprocal of 1 to this gets 49/6 (in reduced form). But 49 is composite. However, adding the reciprocal of 2 to 43/6 gets 23/3 (when written in reduced form). 23 is a prime, so therefore a(10) = 2.
%t a = {1}; s = 1; Do[i = 1; While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[a, i], {80}]; a (* _Stefan Steinerberger_, Oct 27 2007 *)
%Y Cf. A134412, A134413.
%K nonn
%O 1,4
%A _Leroy Quet_, Oct 24 2007
%E More terms from _Stefan Steinerberger_, Oct 27 2007
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