id:A059571 - OEIS Search Results

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From Mertens's conjecture (1): Floor(sqrt(n)) - |Mertens's function A002321(n)|.

+0
4

0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 2, 3, 2, 2, 1, 1, 2, 3, 2, 2, 3, 4, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 5, 6, 6, 5, 4, 3, 3, 3, 4, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 6, 7, 6, 6, 5, 6, 6, 7, 8, 7, 6, 6, 7, 6, 5, 5, 4, 5, 5, 5, 6, 5, 4, 4, 5, 6, 5, 5, 6, 7, 8, 8, 7, 7, 8, 8, 9 (list; graph; listen)

	OFFSET	`1,10`
	COMMENT	`Mertens conjectured that \|A002321(n)\| < sqrt(n) for all n>1. This is now known to be false. So eventually there will be negative terms.`
	REFERENCES	`D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2.` `K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000; p. 267.`
	LINKS	`A. M. Odlyzko and H. J. J. te Riele, Disproof of the Mertens conjecture, J. reine angew. Math., 357 (1985), pp. 138-160.`
	CROSSREFS	`Cf. A059572, A002321, A059581.` `Sequence in context: A131334 A004602 A153764 this_sequence A027052 A144409 A131257` `Adjacent sequences: A059568 A059569 A059570 this_sequence A059572 A059573 A059574`
	KEYWORD	`nonn`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2001`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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