A068101 a(n) = Sum_{k|n, k<=sqrt(n)} mu(k) where mu(k) is the Moebius function and the sum is over the positive divisors k of n with k <= sqrt(n).

1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 1, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, -2, 1, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, 1

Offset: 1

Author

Leroy Quet, Mar 22 2002

Keywords

• sign

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086956.

Programs

Haskell

a068101 = sum . map a008683 . a161906_row
-- Reinhard Zumkeller, Jul 30 2013

Mathematica

Table[DivisorSum[n, MoebiusMu, # <= Sqrt[n] &], {n, 103}] (* Michael De Vlieger, Sep 24 2017 *)

PARI

a(n) = sumdiv(n, k, (k<=sqrt(n))*moebius(k)); \\ Michel Marcus, Jan 03 2017

Formula

a(n) = Sum_{k=1..A038548(n)} A008683(A161906(n,k)). - Reinhard Zumkeller, Jul 30 2013

G.f.: Sum_{k>=1} mu(k)*x^(k^2)/(1 - x^k). - Ilya Gutkovskiy, Jan 03 2017