A282870 - OEIS

A282870

a(n) = floor( Li(n) - pi(n) ).

0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 4, 5, 4, 4, 3, 3, 4, 4

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OFFSET

2,9

COMMENTS

Li(x) is the logarithmic integral of x.

pi(x) is the number of primes less than or equal to x, A000720(x).

"The Riemann hypothesis is an assertion about the size of the error term in the prime number theorem, namely, that pi(x) = li(x)+O(x^(1/2+epsilon))", see Nathanson, page 323.

REFERENCES

Melvyn B. Nathanson, Elementary Methods in Number Theory, Springer, 2000

LINKS

Table of n, a(n) for n=2..106.

FORMULA

a(n) = A047783(n) - A000720(n).

MAPLE

a:= n-> floor(evalf(Li(n)))-numtheory[pi](n):

seq(a(n), n=2..120); # Alois P. Heinz, Feb 23 2017

MATHEMATICA

iend = 100;

For[x = 1, x <= iend, x++,