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%I #33 Aug 07 2021 05:13:19
%S 1,906150258,906150259,906150260,906150263,906150264,906150331,
%T 906150334,906150337,906150338,906150339,906150358,906150359,
%U 906150362,906150363,906150368,906150387,906150388,906150389,906150406,906150407
%N a(n) is least value of m for which the sum of Liouville's function from 1 to m is n.
%C It was once conjectured that the sum of Liouville's function was never > 0 except for the first term.
%C It follows from Theorem 2 in Borwein-Ferguson-Mossinghoff that a(n) < 262*n^2 infinitely often, improving on an earlier result of Anderson & Stark. - _Charles R Greathouse IV_, Jun 14 2011
%C 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
%C 3.75 * 10^14 < a(1160328) <= 23156359315279877168. - _Hiroaki Yamanouchi_, Oct 04 2015
%C From _Jianing Song_, Aug 06 2021: (Start)
%C a(n) is the smallest m such that A002819(m) = n.
%C This sequence is strictly increasing since A002819(m) - A002819(m-1) = A008836(m) = +-1. (End)
%D R. J. Anderson and H. M. Stark, Oscillation theorems, Analytic Number Theory (1980); Lecture Notes in Mathematics 899 (1981), pp. 79-106.
%H Donovan Johnson and Hiroaki Yamanouchi, <a href="/A051470/b051470.txt">Table of n, a(n) for n = 1..100000</a> (terms a(1)-a(829) from _Donovan Johnson_)
%H P. Borwein, R. Ferguson, and M. Mossinghoff, <a href="http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P208.pdf">Sign changes in sums of the Liouville function</a>, Mathematics of Computation 77 (2008), pp. 1681-1694.
%H R. S. Lehman, <a href="http://dx.doi.org/10.1090/S0025-5718-1960-0120198-5">On Liouville's function</a>, Math. Comp., 14 (1960), 311-320.
%H M. Tanaka, <a href="http://dx.doi.org/10.3836/tjm/1270216093">A Numerical Investigation on Cumulative Sum of the Liouville Function</a>, Tokyo J. Math. 3, 187-189, 1980.
%e The sum of Liouville's function from 1 through 906150258 is 2, that is the smallest value, so a(2)=906150258.
%o (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
%Y Cf. A008836 (Liouville's function), A002819, A028488.
%K nonn
%O 1,2
%A _Jud McCranie_
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