A062563 a(n) = Sum_{k=1..n} d(k)* mu(k), where d(k) is the number of divisors function.

1, -1, -3, -3, -5, -1, -3, -3, -3, 1, -1, -1, -3, 1, 5, 5, 3, 3, 1, 1, 5, 9, 7, 7, 7, 11, 11, 11, 9, 1, -1, -1, 3, 7, 11, 11, 9, 13, 17, 17, 15, 7, 5, 5, 5, 9, 7, 7, 7, 7, 11, 11, 9, 9, 13, 13, 17, 21, 19, 19, 17, 21, 21, 21, 25, 17, 15, 15, 19, 11, 9, 9, 7, 11, 11, 11, 15, 7, 5, 5, 5, 9, 7, 7, 11, 15, 19, 19, 17, 17, 21, 21, 25, 29, 33, 33, 31

Offset: 1

Author

Jason Earls, Jul 03 2001

Keywords

• sign

Crossrefs

Partial sums of A226177.

Programs

Mathematica

Accumulate[Table[DivisorSigma[0,n]MoebiusMu[n],{n,100}]] (* Harvey P. Dale, Aug 15 2016 *)

PARI

v=[]; for(n=1,250,v=concat(v,sum(k=1,n,numdiv(k)*moebius(k)))); v

Formula

Also a(n) = Sum_{k=1..n} 2^omega(k)*mu(k). - Benoit Cloitre, Jun 13 2007