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 A282870 a(n) = floor( Li(n) - pi(n) ). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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++, a[x] = N[LogIntegral[x] - PrimePi[x]]]; t = Table[Floor[a[i]], {i, 2, iend}]; Print[t] Table[Floor[LogIntegral[n] - PrimePi[n]], {n, 2, 110}] (* G. C. Greubel, May 17 2019 *) PROG (PARI) vector(110, n, n++; floor(real(-eint1(-log(n))) - primepi(n)) ) \\ G. C. Greubel, May 17 2019 (Magma) [Floor(LogIntegral(n) - #PrimesUpTo(n)): n in [2..110]]; // G. C. Greubel, May 17 2019 (Sage) [floor(li(n) - prime_pi(n)) for n in (2..110)] # G. C. Greubel, May 17 2019 CROSSREFS Cf. A000720, A047783, A052435, A359145. Sequence in context: A026517 A072047 A327521 * A106802 A269254 A049236 Adjacent sequences: A282867 A282868 A282869 * A282871 A282872 A282873 KEYWORD sign AUTHOR David S. Newman, Feb 23 2017 STATUS approved

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Last modified July 25 02:50 EDT 2024. Contains 374585 sequences. (Running on oeis4.)