OFFSET
1,1
COMMENTS
L(n) = (-1)^omega(n) where omega(n) is the number of prime factors of n with multiplicity.
REFERENCES
H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409.
H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55.
LINKS
Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..43 (terms < 10^13, first 38 terms from Donovan Johnson)
Peter Borwein, Ron Ferguson, and Michael J. Mossinghoff, Sign changes in sums of the Liouville function. Math. Comp. 77 (2008), 1681-1694.
R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311-320.
EXAMPLE
a(1) = 2 and L(2) = -1;
a(2) = 2 and L(2) = L(3)= -1;
a(3) = 11 and L(11) = L(12) = L(13) = -1;
a(4) = 17 and L(17) = L(18) = L(19) = L(20) = -1.
MAPLE
with(numtheory):for k from 0 to 30 do : indic:=0:for n from 1 to 1000000000 while (indic=0)do :s:=0:for i from 0 to k do :if (-1)^bigomega(n+i)= -1 then s:=s+1: else fi:od:if s=k+1 and indic=0 then print(n):indic:=1:else fi:od:od:
MATHEMATICA
Table[k=1; While[Sum[LiouvilleLambda[k+i], {i, 0, n-1}]!=-n, k++]; k, {n, 1, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 04 2010
EXTENSIONS
a(15) and a(21) corrected by Donovan Johnson, Apr 01 2013
STATUS
approved