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a(n) = smallest m such that Sum_{i=1..m} 1/sqrt(prime(i)) >= n.
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%I #24 Oct 13 2017 12:45:11

%S 2,4,8,13,21,30,43,58,76,97,121,149,180,214,252,294,340,390,444,502,

%T 564,630,700,775,854,937,1025,1118,1215,1317,1423,1535,1650,1771,1897,

%U 2027,2162,2303,2448,2598,2753,2914,3079,3250,3426,3607,3793,3984,4181,4383,4591,4803,5022,5245,5474,5709

%N a(n) = smallest m such that Sum_{i=1..m} 1/sqrt(prime(i)) >= n.

%H Vincenzo Librandi, <a href="/A292774/b292774.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) ~ (n^2*log(n))/2. - _Benoit Cloitre_, Oct 01 2017 [This follows from the asymptotics for A292775]

%p Digits:=50;

%p s0:=0; k:=1; lisi:=[]; lisP:=[];

%p for i from 1 to 10000 do p:=ithprime(i);

%p s0:=s0+evalf(1/sqrt(p));

%p if s0 >= k then k:=k+1; lisi:=[op(lisi),i]; lisP:=[op(lisP),p]; fi;

%p od:

%p lisi; # A292774

%p lisP; # A292775

%t f[n_]:=Block[{k=0, s=0}, While[s<n, k++; s=N[s+1/Sqrt[Prime[k]], 50]]; k]; Table[f[n], {n, 1, 60}] (* _Vincenzo Librandi_, Oct 01 2017 *)

%Y Cf. A292775; A019529, A054040.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 30 2017