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Integer part of the sum of the inverses of the first n primes.
1

%I #34 Feb 08 2024 12:44:45

%S 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2

%N Integer part of the sum of the inverses of the first n primes.

%C The sequence is unbounded.

%H Carl Erickson, <a href="http://people.brandeis.edu/~cwe/pdfs/primes_and_riemann.pdf">Prime Numbers and the Riemann Hypothesis</a>

%F a(n) = floor(Sum_{i=1..n} 1/A000040(i)).

%F a(n) = floor(A024451(n)/A002110(n)). - _Antti Karttunen_, Feb 08 2024

%t Table[Floor@Sum[1/(Prime[j]), {j, 1, n}], {n, 1, 120}]

%Y Cf. A002110, A024451, A046024 (places of records).

%K nonn

%O 1,59

%A _Andres Cicuttin_, Jun 19 2016