A140254 Mobius transform of A014963.

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

Offset: 1

Author

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

Keywords

• sign

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.

Examples

			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.
		

Links

• Physics Forums discussion, Moebius function.
• Eric. W. Weisstein, Mertens Conjecture.

Crossrefs

Cf. A014963, A008683, A140255, A140256.

Formula

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

Extensions

More terms from Mats Granvik, Jun 29 2008