A328556 Expansion of Product_{p prime, k>=1} (1 - x^(p^k)).
1, 0, -1, -1, -1, 0, 1, 1, 0, 0, 1, 1, 1, 0, -1, -1, -2, -1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, -3, -3, -1, 1, 1, 0, -1, -1, 2, 2, 0, 1, -1, 0, 1, 0, -1, 0, 1, 0, 0, -2, -3, -1, -1, 0, 2, 0, 1, 3, 0, 1, 3, 1, -3, -2, -3, -2, 3, 2, -1, 0, -2, 1, 1, -2, -1, 1, 2, 2, 3, -1, -2, 4
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
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Maple
N:= 100: # for a(0)..a(N) R:= 1: p:= 1: do p:= nextprime(p); if p > N then break fi; for k from 1 to floor(log[p](N)) do R:= series(R*(1-x^(p^k)),x,N+1) od; od: seq(coeff(R,x,j),j=0..N); # Robert Israel, Nov 03 2019 -
Mathematica
nmax = 90; CoefficientList[Series[Product[(1 - Boole[PrimePowerQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[Boole[PrimePowerQ[d]] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 90}]
Formula
G.f.: Product_{k>=1} (1 - x^A246655(k)).
Comments