A284835 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j), where mu() is the Moebius function (A008683).
1, 3, 5, 8, 11, 18, 22, 31, 39, 53, 64, 87, 104, 134, 165, 205, 248, 310, 368, 455, 545, 659, 784, 947, 1117, 1337, 1579, 1872, 2197, 2604, 3036, 3570, 4168, 4866, 5661, 6599, 7633, 8859, 10236, 11831, 13625, 15715, 18036, 20728, 23761, 27211, 31106, 35560, 40533, 46221, 52596, 59813, 67912, 77090, 87343
Offset: 1
Keywords
Examples
a(5) = 11 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 1 + 2 + 1 + 5 = 11.
Programs
-
Mathematica
nmax = 55; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i) Product[1/(1 - MoebiusMu[j]^2 x^j), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]] -
PARI
x='x+O('x^56); Vec(sum(i=1, 56, moebius(i)^2*x^i/(1 - x^i) * prod(j=1, i, 1/(1 - moebius(j)^2*x^j)))) \\ Indranil Ghosh, Apr 04 2017
Formula
G.f.: Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j).
Comments