A081240 #{(i,j): mu(i)*mu(j) = 1, 1<=i,j<=n}, where mu=A008683 (Moebius function).

1, 2, 5, 5, 10, 13, 20, 20, 20, 25, 34, 34, 45, 52, 61, 61, 74, 74, 89, 89, 100, 113, 130, 130, 130, 145, 145, 145, 164, 185, 208, 208, 225, 244, 265, 265, 290, 313, 338, 338, 365, 394, 425, 425, 425, 452, 485, 485, 485, 485, 514, 514, 549, 549, 580, 580, 613

Offset

1,2

Comments

A081238(n) + A081239(n) + a(n) = n^2;

a(n) = a(n-1) iff mu(n) = 0.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..520

Formula

a(n) = |sum(i=1..n, sqrt(mu(i))|^2. - Enrique Pérez Herrero, Jul 30 2012

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)=20, as there are
6 .. +1 ..... | + - - 0 - + - 0 20 '+1's in the 8x8-square
7 .. -1 ..... | - + + 0 + - + 0 (represented as '+')
8 ... 0 ..... | 0 0 0 0 0 0 0 0.

Mathematica

Table[Abs[Sum[Sqrt[MoebiusMu[i]], {i, 1, n}]]^2, {n, 60}] (* Enrique Pérez Herrero, Jul 30 2012 *)

Prog

(Haskell)
a081240 n = length [() | u <- [1..n], v <- [1..n],
                         a008683 u * a008683 v == 1]
-- Reinhard Zumkeller, Aug 03 2012

Crossrefs

Cf. A070548.

Sequence in context: A351475 A034387 A349803 * A184443 A238655 A132295

Adjacent sequences: A081237 A081238 A081239 * A081241 A081242 A081243

Keyword

nonn

Author

Reinhard Zumkeller, Mar 11 2003

Status

approved