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A189229 Counterexamples to Polya's conjecture that A002819(n) <= 0 if n > 1. 3
906150257, 906150258, 906150259, 906150260, 906150261, 906150262, 906150263, 906150264, 906150265, 906150266, 906150267, 906150268, 906150269, 906150270, 906150271, 906150272, 906150273, 906150274, 906150275, 906150276, 906150277, 906150278, 906150279, 906150280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

906150294 is the smallest number > 906150257 that is not in the sequence (see A028488).

See A002819, A008836, A028488, A051470 for additional comments, references, and links.

See Brent and van de Lune (2011) for a history of Polya's conjecture and a proof that it is true "on average" in a certain precise sense.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

R. P. Brent and J. van de Lune, A note on Polya's observation concerning Liouville's function, arXiv 2011.

M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3 (1980), 187-189.

Wikipedia, Pólya conjecture

FORMULA

(n-1)*A002819(n) > 0

EXAMPLE

906150257 is the smallest number n > 1 with A002819(n) > 0 - (see Tanaka 1980).

PROG

(PARI) s=1; c=0; for(n=2, 906188859, s=s+(-1)^bigomega(n); if(s>0, c++; write("b189229.txt", c " " n))) /* Donovan Johnson, Apr 25 2013 */

CROSSREFS

Cf. A002819 (Liouville's summatory function L(n)), A008836 (Liouville's function lambda(n)), A028488 (n such that L(n) = 0), A051470 (least m for which L(m) = n).

Sequence in context: A210299 A178557 A157798 * A051470 A076135 A015382

Adjacent sequences:  A189226 A189227 A189228 * A189230 A189231 A189232

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Jun 13 2011

STATUS

approved

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Last modified April 27 15:06 EDT 2017. Contains 285528 sequences.