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Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/6.
1

%I #16 Mar 27 2019 19:13:22

%S 1,1,1,2,2,3,4,6,10,16,29,59,140,400,1413,6467,40261,361139,4990906,

%T 114916199,4833601540

%N Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/6.

%C a(22) > 5*10^10. - _Robert Price_, Dec 10 2013

%t For[n = 1, n ≤ 17, n++, sum = 0; For[k = 1, k ≤ 10^6, k++, sum = sum + 1/Prime[k]; If[sum >= n/6, Print[k]; Break[]]]] (* _Robert Price_, Dec 09 2013 *)

%t Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/6, m++];

%t m, {n, 1, 17}] (* _Robert Price_, Mar 27 2019 *)

%Y Cf. A016088, A046024, A103591-A103600.

%K nonn

%O 1,4

%A _James R. Buddenhagen_, Mar 28 2005

%E a(2)-a(4) and a(19)-a(21) added by _Robert Price_, Dec 10 2013