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

1,4

Comments

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

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

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A057627.

Sequence in context: A162018 A055741 A103621 * A264814 A029612 A120165

Adjacent sequences: A081236 A081237 A081238 * A081240 A081241 A081242

Keyword

nonn

Author

Reinhard Zumkeller, Mar 11 2003

Status

approved