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A084234 Smallest k such that |M(k)| = n^2, where M(x) is Mertens's function A002321. 1
1, 31, 443, 1637, 2803, 9749, 19111, 24110, 42833, 59426, 95514, 230227, 297335, 297573, 299129, 355541, 897531, 924717, 926173, 1062397, 1761649, 1763079, 1789062, 3214693, 3218010, 3232958, 4962865, 5307549, 5343710, 6433477 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..30.

MATHEMATICA

i = s = 0; Do[While[Abs[s] < n^2, s = s + MoebiusMu[i]; i++ ]; Print[i - 1], {n, 1, 25}]

CROSSREFS

Cf. A051402.

Sequence in context: A278964 A010836 A022723 * A187622 A187630 A118196

Adjacent sequences:  A084231 A084232 A084233 * A084235 A084236 A084237

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, May 13 2003

STATUS

approved

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Last modified December 18 10:43 EST 2018. Contains 318219 sequences. (Running on oeis4.)