A391803 a(n) = floor(Sum_{k=1..n} n/prime(k)).

0, 1, 3, 4, 6, 8, 9, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 66, 68, 70, 72, 74, 76, 78, 80, 83, 85, 87, 89, 91, 93, 96, 98, 100, 102, 104, 107, 109, 111, 113, 115, 118, 120, 122, 124, 127

Offset

1,3

Comments

a(n+1) - a(n) <= 3 for n < 128022.

Links

Table of n, a(n) for n=1..63.

Example

a(3) = floor(3/2 + 3/3 + 3/5) = 3.

Mathematica

z = 160; p[n_] := p[n] = Prime[n];
s[n_] := Floor[Total[n/p[Range[n]]]];
Table[s[n], {n, 1, z}]

Prog

(Python)
from sympy import nextprime
from fractions import Fraction
from itertools import count, islice
def agen(): # generator of terms
    S, p = 0, 2
    for n in count(1):
        S, p = S + Fraction(1, p), nextprime(p)
        yield int(n*S)
print(list(islice(agen(), 63))) # Michael S. Branicky, Dec 31 2025

Crossrefs

Cf. A000040, A046024.

Sequence in context: A138097 A193732 A000592 * A138924 A188015 A192284

Adjacent sequences: A391800 A391801 A391802 * A391804 A391805 A391806

Keyword

nonn

Author

Clark Kimberling, Dec 31 2025

Status

approved