OFFSET
1,2
COMMENTS
"[I]f the absolute value of M(n) can be proved to be always less than the square root of n, then the Riemann Hypothesis is true. This is called Mertens's conjecture. ... Then along came Andrew Odlyzko and his colleague, Herman te Riele and they showed in 1984 that there is a number, far larger than 10^30, that invalidates Mertens's conjecture - call it N. In other words, M(N) is greater than the square of N. So the conjecture is not true." [Sabbagh]
REFERENCES
Karl Sabbagh, The Riemann Hypothesis, The Greatest Unsolved Problem in Mathematics, Farrar, Straus and Giroux, New York, 2002, page 191.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..100 (calculated using the b-file at A051402)
FORMULA
a(n) = A051402(n^2). - Amiram Eldar, May 06 2024
MATHEMATICA
i = s = 0; Do[While[Abs[s] < n^2, s = s + MoebiusMu[i]; i++ ]; Print[i - 1], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, May 13 2003
EXTENSIONS
a(31)-a(34) from Amiram Eldar, May 06 2024
STATUS
approved