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
According to Pólya, numbers (p-3)/4 are members of this sequence, with p a Heegner number > 7 (that is, p is one of 11, 19, 43, 67, and 163). - Friedjof Tellkamp, Feb 15 2025
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.
G. Pólya, Verschiedene Bemerkungen zur Zahlentheorie, Jahresber. DMV 28, 31-40, 1919.
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
KEYWORD
nonn,nice,changed
AUTHOR
EXTENSIONS
More terms from Hans Havermann, Jun 24 2002
STATUS
approved