A081239 #{(i,j): mu(i)*mu(j) = 0, 1<=i,j<=n}, where mu=A008683 (Moebius function).

0, 0, 0, 7, 9, 11, 13, 28, 45, 51, 57, 80, 88, 96, 104, 135, 145, 180, 192, 231, 245, 259, 273, 320, 369, 387, 440, 495, 517, 539, 561, 624, 648, 672, 696, 767, 793, 819, 845, 924, 952, 980, 1008, 1095, 1184, 1216, 1248, 1343, 1440, 1539, 1577, 1680, 1720

Offset: 1

Author

Reinhard Zumkeller, Mar 11 2003

Keywords

• nonn

Comments

A081238(n) + a(n) + A081240(n) = n^2;

a(n) = a(n-1) + 2*n + 1 iff mu(n) = 0.

Examples

			n mu(n) ... n: 1 2 3 4 5 6 7 8
- ------ .... |----------------
1 .. +1 ..... | + - - 0 - + - 0
2 .. -1 ..... | - + + 0 + - + 0
3 .. -1 ..... | - + + 0 + - + 0
4 ... 0 ..... | 0 0 0 0 0 0 0 0
5 .. -1 ..... | - + + 0 + - + 0 a(8)=28, as there are
6 .. +1 ..... | + - - 0 - + - 0 28 '0's in the 8x8-square
7 .. -1 ..... | - + + 0 + - + 0
8 ... 0 ..... | 0 0 0 0 0 0 0 0.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A057627.

Programs

Haskell

a081239 n = length [() | u <- [1..n], v <- [1..n],
                         a008683 u * a008683 v == 0]
-- Reinhard Zumkeller, Aug 03 2012

Formula

a(n) = n^2 - A013928(n+1)^2. - Vladeta Jovovic, Mar 12 2003