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

1,59

Comments

The sequence is unbounded.

Links

Table of n, a(n) for n=1..96.

Carl Erickson, Prime Numbers and the Riemann Hypothesis

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A343643 A044928 A362114 * A178489 A044929 A000520

Adjacent sequences: A274067 A274068 A274069 * A274071 A274072 A274073

Keyword

nonn

Author

Andres Cicuttin, Jun 19 2016

Status

approved