0,9

Short history of conjecture L(n) <= 0 for all n >= 2 by Deborah Tepper Haimo. George Polya conjectured 1919 that L(n) <= 0 for all n >= 2. The conjecture was generally deemed true for nearly 40 years, until 1958, when C. B. Haselgrove proved that L(n) > 0 for infinitely many n. In 1962, R. S. Lehman found that L(906180359) = 1 and in 1980, M. Tanaka discovered that the smallest counterexample of the Polya conjecture occurs when n = 906150257. - Harri Ristiniemi (harri.ristiniemi(AT)nicf.), Jun 23 2001

Prime number theorem is equivalent to a(n)=o(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003

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.

D. T. Haimo, Experimentation and Conjecture Are Not Enough, The American Mathematical Monthly Volume 102 Number 2, 1995, page 105.

R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311-320.

M. Tanaka, A numerical investigation on cumulative sum of the Liouville function, Tokyo J. Math. 3 (1980), 187-189.

T. D. Noe, Table of n, a(n) for n=0..10000

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

(PARI) a(n)=sum(i=1, n, (-1)^bigomega(i))

Cf. A008836, A002053, A028488.

Sequence in context: A116433 A106509 A053615 this_sequence A037834 A004074 A053646

Adjacent sequences: A002816 A002817 A002818 this_sequence A002820 A002821 A002822

nice,sign,easy

njas

More terms from Larry Reeves (larryr(AT)acm.org), Jul 09 2001