A348510 a(n) = A099377(n) - n, where A099377(n) is the numerator of the harmonic mean of the divisors of n.

0, 2, 0, 8, 0, -4, 0, 24, 18, 10, 0, 6, 0, -7, -10, 64, 0, 18, 0, 0, 0, 0, 0, -8, 50, 26, 0, -25, 0, -20, 0, 32, -22, 34, 0, 288, 0, 0, 0, -8, 0, -35, 0, -22, 0, -23, 0, 72, 0, 50, -34, 104, 0, -36, 0, 0, 0, 58, 0, -30, 0, -31, 126, 384, 0, -55, 0, 0, -46, -35, 0, 216, 0, 74, 150, 38, 0, -52, 0, 320, 324, 82, 0, -75

Offset: 1

Author

Antti Karttunen, Oct 31 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A099377, A250094 (positions of zeros), A348968, A348969.

Programs

Mathematica

a[n_] := Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]] - n; Array[a, 100] (* Amiram Eldar, Oct 31 2021 *)

PARI

A099377(n) = { my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); }; \\  From A099377
A348510(n) = (A099377(n)-n);