A208769 Dirichlet inverse of the finite group count (A000001).
1, -1, -1, -1, -1, 0, -1, -2, -1, 0, -1, 0, -1, 0, 1, -5, -1, 0, -1, 0, 0, 0, -1, -1, -1, 0, -2, 1, -1, 0, -1, -23, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 1, 1, 0, -1, -8, -1, 0, 1, 0, -1, -1, 0, -1, 0, 0, -1, 0, -1, 0, 1, -159, 1, 0, -1, 0, 1, 0, -1, -6, -1, 0, 0, 1, 1, 0, -1, -10, -6, 0, -1, 1, 1, 0, 1, 0, -1, 0, 1, 1, 0, 0, 1, -60, -1, 0, 1, -2, -1, 0, -1, 0
Offset: 1
Links
- Antti Karttunen, Table of n, a(n) for n = 1..2047 (computed from the b-file of A000001; a(1024) corrected by Andrey Zabolotskiy)
- Wikipedia, Dirichlet convolution (Dirichlet inverse)
Programs
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Mathematica
a[1] = 1; a[n_] := a[n] = -Sum[FiniteGroupCount[n/k] a[k], {k, Drop[Divisors[n], -1]}]; Table[a[n], {n, 100}] -
PARI
v000001 = readvec("b000001_to.txt"); \\ Prepared with gawk ' { print $2 } ' from the b-file of A000001. A000001(n) = v000001[1+n]; A208769(n) = if(1==n,1,-sumdiv(n,d,if(d
Formula
a(1) = 1; for n > 1, a(n) = -Sum_{d|n, dA000001(n/d)*a(d). - Antti Karttunen, Jun 13 2018
Extensions
More terms from Antti Karttunen, Jun 13 2018