

A051470


a(n) is least value of m for which the sum of Liouville's function from 1 to m is n.


9



1, 906150258, 906150259, 906150260, 906150263, 906150264, 906150331, 906150334, 906150337, 906150338, 906150339, 906150358, 906150359, 906150362, 906150363, 906150368, 906150387, 906150388, 906150389, 906150406, 906150407
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OFFSET

1,2


COMMENTS

It was once conjectured that the sum of Liouville's function was never > 0 except for the first term.
It follows from Theorem 2 in BorweinFergusonMossinghoff that a(n) < 262*n^2 infinitely often, improving on an earlier result of Anderson & Stark.  Charles R Greathouse IV, Jun 14 2011
a(830) > 2 * 10^14 (probably around 3.511e14) and a(1160327) = 351753358289465 according to the calculations of Borwein, Ferguson, & Mossinghoff.  Charles R Greathouse IV, Jun 14 2011
3.75 * 10^14 < a(1160328) <= 23156359315279877168.  Hiroaki Yamanouchi, Oct 04 2015


REFERENCES

R. J. Anderson and H. M. Stark, Oscillation theorems, Analytic Number Theory (1980); Lecture Notes in Mathematics 899 (1981), pp. 79106.


LINKS

Donovan Johnson and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100000 (terms a(1)a(829) from Donovan Johnson)
P. Borwein, R. Ferguson, and M. Mossinghoff, Sign changes in sums of the Liouville function, Mathematics of Computation 77 (2008), pp. 16811694.
R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311320.
M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3, 187189, 1980.


EXAMPLE

The sum of Liouville's function from 1 through 906150258 is 2, that is the smallest value, so a(2)=906150258.


PROG

(PARI) print1(r=1); t=0; for(n=906150257, 906400000, t+=(1)^bigomega(n); if(t>r, r=t; print1(", "n))) \\ Charles R Greathouse IV, Jun 14 2011


CROSSREFS

Cf. A028488.
Sequence in context: A157798 A328135 A189229 * A076135 A015382 A115385
Adjacent sequences: A051467 A051468 A051469 * A051471 A051472 A051473


KEYWORD

nonn


AUTHOR

Jud McCranie


STATUS

approved



