

A140254


Mobius transform of A014963.


5



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
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OFFSET

1,3


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.


LINKS

Table of n, a(n) for n=1..77.
Physics Forums discussion, Moebius function.
Eric. W. Weisstein, Mertens Conjecture.


FORMULA

A054525 as an infinite lower triangular matrix * A014963 as a vector.


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.


CROSSREFS

Cf. A014963, A008683, A140255, A140256.
Sequence in context: A122512 A128263 A241384 * A204187 A095202 A291937
Adjacent sequences: A140251 A140252 A140253 * A140255 A140256 A140257


KEYWORD

sign


AUTHOR

Gary W. Adamson and Mats Granvik, May 16 2008, Jun 29 2008


EXTENSIONS

More terms from Mats Granvik, Jun 29 2008


STATUS

approved



