This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028488 #56 Mar 05 2025 09:03:19
%S A028488 2,4,6,10,16,26,40,96,586,906150256,906150294,906150308,906150310,
%T A028488 906150314,906151516,906151576,906152172,906154582,906154586,
%U A028488 906154590,906154594,906154604,906154606,906154608,906154758,906154760,906154762
%N A028488 Numbers k such that the summatory Liouville function L(k) (A002819) is zero.
%C A028488 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 A028488 L(23156358837978983978) = 0 and L(k) < 0 for k from 2.3156354*10^19 to 23156358837978983977. - _Hiroaki Yamanouchi_, Oct 03 2015
%C A028488 All terms are even since k and A002819(k) have the same parity. - _Jianing Song_, Aug 06 2021
%C A028488 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
%H A028488 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 A028488 P. Borwein, R. Ferguson, and M. Mossinghoff, <a href="https://doi.org/10.1090/S0025-5718-08-02036-X">Sign changes in sums of the Liouville function</a>, Mathematics of Computation 77 (2008), pp. 1681-1694.
%H A028488 G. Pólya, <a href="https://eudml.org/doc/145560">Verschiedene Bemerkungen zur Zahlentheorie</a>, Jahresber. DMV 28, 31-40, 1919.
%H A028488 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 A028488 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 A028488 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LiouvilleFunction.html">Liouville Function</a>
%H A028488 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolyaConjecture.html">Polya Conjecture</a>
%p A028488 B:= [seq((-1)^numtheory:-bigomega(i),i=1..10^5)]:
%p A028488 L:= ListTools:-PartialSums(B):
%p A028488 select(t -> L[t]=0, [$1..10^5]); # _Robert Israel_, Aug 27 2015
%t A028488 Position[Table[Sum[LiouvilleLambda@ k, {k, 1, n}], {n, 1000}], n_ /; n == 0] // Flatten (* _Michael De Vlieger_, Aug 27 2015 *)
%t A028488 Position[Accumulate[LiouvilleLambda[Range[1000]]],0]//Flatten (* _Harvey P. Dale_, Aug 10 2022 *)
%Y A028488 Cf. A008836 (Liouville's function), A002819, A051470.
%Y A028488 Cf. A003173 (Heegner numbers).
%K A028488 nonn,nice
%O A028488 1,1
%A A028488 _Eric W. Weisstein_
%E A028488 More terms from _Hans Havermann_, Jun 24 2002