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A140254
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Mobius transform of A014963.
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3
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1, 1, 2, 0, 4, -3, 6, 0, 0, -5, 10, 0, 12, -7, -6, 0, 16, 0, 18, 0, -8, -11, 22, 0, 0, -13, 0, 0, 28, 7, 30, 0, -12, -17, -10, 0, 36, -19, -14, 0, 40, 9, 42, 0, 0, -23, 46, 0, 0, 0, -18, 0, 52, 0, -14, 0, -20, -29, 58, 0, 60, -31, 0, 0, -16, 13, 66, 0, -24, 11, 70, 0, 72, -37, 0, 0, -16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Conjectures relating to the Mobius sequence A008683:
If mu(n) = 0, a(n) = 0.
If mu(n) = 1, (n>1), a(n) = a negative term.
If mu(n) = -1, a(n) = a positive term.
So except for the first term and zero divided by zero we would have mu(n) = -a(n)/abs(a(n)).
Examples: mu(4) = 0, a(4) = 0; mu(6) = 1, a(6) = (-3); mu(7) = (-1), a(7) = 6.
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LINKS
| Physics Forums discussion, Moebius function.
Eric. W. Weisstein, Mertens Conjecture.
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FORMULA
| A054525 as an infinite lower triangular matrix * A014963 as a vector.
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EXAMPLE
| a(5) = -3 = (1, -1, -1, 0, 0, 1) dot (1, 2, 3, 2, 5, 1) = (1 - 2 - 3 + 0 + 0 + 1), where (1, -1, -1, 0, 0, 1) = row 5 of triangle A054525 and (1, 2, 3, 2, 5, 1) = the first 5 terms of A014963.
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CROSSREFS
| Cf. A014963, A008683, A140255, A140256.
Sequence in context: A088330 A122512 A128263 * A204187 A095202 A154849
Adjacent sequences: A140251 A140252 A140253 * A140255 A140256 A140257
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KEYWORD
| sign
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AUTHOR
| Gary W. Adamson and Mats Granvik (qntmpkt(AT)yahoo.com), May 16 2008, Jun 29 2008
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EXTENSIONS
| More terms from Mats Granvik (mgranvik(AT)abo.fi), Jun 29 2008
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