A334895 G.f.: (Sum_{k>=1} prime(k) * x^k) * (Product_{j>=1} (1 - x^j)).
0, 2, 1, 0, -1, -1, -3, -4, -4, -3, 3, -1, 5, 3, 2, 6, 8, 11, 3, 3, 1, -5, -5, -3, -4, -8, -12, -16, -19, -13, -5, 9, 3, 1, -7, 3, 7, 0, 20, 18, 18, 18, 23, 19, 15, 9, 5, 5, 15, -9, -25, -27, -25, -20, -6, -12, -20, -10, -20, -17, -27, -9, -1, 5, -5, -13, -23, 3, 1, 15, 19
Offset: 0
Keywords
Links
- Ilya Gutkovskiy, Scatter plot of a(n) up to n=10000
Crossrefs
Programs
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Mathematica
nmax = 70; CoefficientList[Series[Sum[Prime[k] x^k, {k, 1, nmax}] Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x] A010815[0] = 1; A010815[n_] := A010815[n] = -(1/n) Sum[DivisorSigma[1, k] A010815[n - k], {k, 1, n}]; a[n_] := Sum[Prime[k] A010815[n - k], {k, 1, n}]; Table[a[n], {n, 0, 70}]
Formula
Sum_{k=1..n} a(k) * A000041(n-k) = prime(n).
Comments