A068101 - OEIS

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

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OFFSET

1,30

LINKS

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

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

MATHEMATICA

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

PROG

(Haskell)