A028488 Numbers k such that the summatory Liouville function L(k) (A002819) is zero.

2, 4, 6, 10, 16, 26, 40, 96, 586, 906150256, 906150294, 906150308, 906150310, 906150314, 906151516, 906151576, 906152172, 906154582, 906154586, 906154590, 906154594, 906154604, 906154606, 906154608, 906154758, 906154760, 906154762

Offset

1,1

Comments

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

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

All terms are even since k and A002819(k) have the same parity. - Jianing Song, Aug 06 2021

Links

Donovan Johnson and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..317312 (a(1)-a(252) from Donovan Johnson)

P. Borwein, R. Ferguson, and M. Mossinghoff, Sign changes in sums of the Liouville function, Mathematics of Computation 77 (2008), pp. 1681-1694.

M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3, 187-189, 1980.

Hiroaki Yamanouchi, Values of L(n) from 2*10^14 to 3.75*10^14 (interval = 5*10^9)

Eric Weisstein's World of Mathematics, Liouville Function

Eric Weisstein's World of Mathematics, Polya Conjecture

Maple

B:= [seq((-1)^numtheory:-bigomega(i), i=1..10^5)]:
L:= ListTools:-PartialSums(B):
select(t -> L[t]=0, [$1..10^5]); # Robert Israel, Aug 27 2015

Mathematica

Position[Table[Sum[LiouvilleLambda@ k, {k, 1, n}], {n, 1000}], n_ /; n == 0] // Flatten (* Michael De Vlieger, Aug 27 2015 *)
Position[Accumulate[LiouvilleLambda[Range[1000]]], 0]//Flatten (* Harvey P. Dale, Aug 10 2022 *)

Crossrefs

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

Sequence in context: A017985 A327474 A347207 * A280341 A227572 A080432

Adjacent sequences: A028485 A028486 A028487 * A028489 A028490 A028491

Keyword

nonn,nice

Author

Eric W. Weisstein

Extensions

More terms from Hans Havermann, Jun 24 2002

Status

approved