A084237 a(n) = M(10^n), where M(n) is Mertens's function.

1, -1, 1, 2, -23, -48, 212, 1037, 1928, -222, -33722, -87856, 62366, 599582, -875575, -3216373, -3195437, -21830254, -46758740, 899990187, 461113106, -3395895277, -2061910120, 62467771689

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Bernardo Boncompagni, Selected values of the Mertens function.

Eugene Kuznetsov, Computing the Mertens function on a GPU, arXiv:1108.0135 [math.NT], 2011.

Harald A. Helfgott and Lola Thompson, Summing mu(n): a faster elementary algorithm, arXiv:2101.08773 [math.NT], 2021.

Eric Weisstein's World of Mathematics, Mertens Function.

Formula

Mertens's function: Sum_{k=1..n} mu(k), where mu = Möbius function (A008683).

a(n) = A002321(10^n).

Mathematica

s = 0; i = 1; Do[ While[i <= 10^n, s = s + MoebiusMu[i]; i++ ]; Print[s], {n, 0, 50}]

Prog

(Perl) use ntheory ":all"; say mertens(10**$_) for 0..15; # Dana Jacobsen, May 22 2015

Crossrefs

Cf. A002321, A008683.

Sequence in context: A054679 A057621 A074809 * A106928 A070934 A296272

Adjacent sequences: A084234 A084235 A084236 * A084238 A084239 A084240

Keyword

sign,more

Author

Robert G. Wilson v, May 15 2003

Extensions

More terms from Eric W. Weisstein, Jun 27 2003

a(17) from Bernardo Boncompagni, Jul 06 2011

Corrected a(17) and added a(18)-a(22) from Eugene Kuznetsov, a(17)-a(19) independently confirmed by Richard Sladkey, Aug 28 2012

a(21)'s sign correction and a(23) from Helfgott and Thompson (2021) added by Amiram Eldar, May 21 2021

Status

approved