A334895 - OEIS

%I #6 May 15 2020 09:58:01

%S 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,

%T -16,-19,-13,-5,9,3,1,-7,3,7,0,20,18,18,18,23,19,15,9,5,5,15,-9,-25,

%U -27,-25,-20,-6,-12,-20,-10,-20,-17,-27,-9,-1,5,-5,-13,-23,3,1,15,19

%N G.f.: (Sum_{k>=1} prime(k) * x^k) * (Product_{j>=1} (1 - x^j)).

%C Convolution of primes with A010815.

%H Ilya Gutkovskiy, <a href="/A334895/a334895.jpg">Scatter plot of a(n) up to n=10000</a>

%F Sum_{k=1..n} a(k) * A000041(n-k) = prime(n).

%t nmax = 70; CoefficientList[Series[Sum[Prime[k] x^k, {k, 1, nmax}] Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]

%t 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}]

%Y Cf. A000040, A000041, A010815, A086717, A246575 (convolution of nonnegative integers with A010815).

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, May 14 2020