A028488 - OEIS

%I #49 Aug 10 2022 19:57:56

%S 2,4,6,10,16,26,40,96,586,906150256,906150294,906150308,906150310,

%T 906150314,906151516,906151576,906152172,906154582,906154586,

%U 906154590,906154594,906154604,906154606,906154608,906154758,906154760,906154762

%N Numbers k such that the summatory Liouville function L(k) (A002819) is zero.

%C a(253) > 2*10^14 according to the calculations of Borwein, Ferguson, & Mossinghoff. Most likely a(253) = 351100332278250. - _Charles R Greathouse IV_, Jun 14 2011

%C L(23156358837978983978) = 0 and L(k) < 0 for k from 2.3156354*10^19 to 23156358837978983977. - _Hiroaki Yamanouchi_, Oct 03 2015

%C All terms are even since k and A002819(k) have the same parity. - _Jianing Song_, Aug 06 2021

%H Donovan Johnson and Hiroaki Yamanouchi, <a href="/A028488/b028488.txt">Table of n, a(n) for n = 1..317312</a> (a(1)-a(252) 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 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.

%H Hiroaki Yamanouchi, <a href="/A028488/a028488.txt">Values of L(n) from 2*10^14 to 3.75*10^14 (interval = 5*10^9)</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LiouvilleFunction.html">Liouville Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolyaConjecture.html">Polya Conjecture</a>

%p B:= [seq((-1)^numtheory:-bigomega(i),i=1..10^5)]:

%p L:= ListTools:-PartialSums(B):

%p select(t -> L[t]=0, [$1..10^5]); # _Robert Israel_, Aug 27 2015

%t Position[Table[Sum[LiouvilleLambda@ k, {k, 1, n}], {n, 1000}], n_ /; n == 0] // Flatten (* _Michael De Vlieger_, Aug 27 2015 *)

%t Position[Accumulate[LiouvilleLambda[Range[1000]]],0]//Flatten (* _Harvey P. Dale_, Aug 10 2022 *)

%Y Cf. A008836 (Liouville's function), A002819, A051470.

%K nonn,nice

%O 1,1

%A _Eric W. Weisstein_

%E More terms from _Hans Havermann_, Jun 24 2002