A274070 Integer part of the sum of the inverses of the first n primes.

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, 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, 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

Offset: 1

Author

Andres Cicuttin, Jun 19 2016

Keywords

• nonn

Comments

The sequence is unbounded.

Links

• Carl Erickson, Prime Numbers and the Riemann Hypothesis

Crossrefs

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

Programs

Mathematica

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

Formula

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

a(n) = floor(A024451(n)/A002110(n)). - Antti Karttunen, Feb 08 2024