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From Von Sterneck's conjecture: Floor(sqrt(n)) - 2*|Mertens's function A002321(n)|.

+0
2

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

	OFFSET	`1,5`
	COMMENT	`Von Sterneck conjectured that 2*\|A002321(n)\| < sqrt(n) for all sufficiently large n. This is now known to be false. This is different from the Mertens conjecture that \|A002321(n)\| < sqrt(n) for all n >1 (which is also false.)`
	REFERENCES	`D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VI.2, p. 188.`
	CROSSREFS	`Cf. A059571, A002321.` `Sequence in context: A082115 A099751 A058728 this_sequence A061895 A129678 A023604` `Adjacent sequences: A059578 A059579 A059580 this_sequence A059582 A059583 A059584`
	KEYWORD	`sign`
	AUTHOR	`njas, Feb 16 2001`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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