A236441 Möbius inversion of A235342.

0, 1, 0, 1, -2, 0, -1, 1, 0, 0, -2, 0, -2, 0, 0, 1, -2, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 7, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 5, 0, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2

Offset: 1

Author

Alexander Riasanovsky, Jan 25 2014

Keywords

• sign

Comments

Möbius inversion of A235342. Since b(xy) = b(x)+b(y) where b = A235342, it follows that a(n) is zero on nonprime powers and b(p) if n=p^k.

Examples

			a(1)=0 since 1 is not a prime power.
a(2)=b(2)=1 since 2=2! and b(2!)=1.
a(3)=b(3)=0 since 3=3!/2! and b(3!/2!)=b(3!)-b(2!)=1-1=0.
a(4)=b(2)=1 (above).
a(5)=b(5)=-2 since 5=5!/(3!2!2!) and b(5!/(3!2!2!))=1-3=-2.
a(6)=0 since 6 is not a prime power.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5041
• Alexander Riasanovsky, Sage program

Crossrefs

Möbius inversion of A235342.

Formula

For n > 0, a(n) = Sum_{d|n} b(d)*mu(n/d) where b(n) = A235342(n).

Extensions

Data section extended and b-file computed with Riasanovsky's Sage program by Antti Karttunen, Mar 28 2017