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URL: https://oeis.org/A028488

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A028488
Numbers k such that the summatory Liouville function L(k) (A002819) is zero.
13
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
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.
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.
Cf. A003173 (Heegner numbers).
Sequence in context: A017985 A327474 A347207 * A280341 A227572 A080432
KEYWORD
nonn,nice
EXTENSIONS
More terms from Hans Havermann, Jun 24 2002
STATUS
approved