A303073 - OEIS

%I #4 Apr 18 2018 09:37:26

%S 2,2,5,2,12,-13,16,-30,41,-18,46,-73,132,-278,315,-318,580,-805,1218,

%T -1998,2665,-3958,5936,-7761,11612,-17678,25313,-38134,54754,-76833,

%U 114392,-166334,240685,-356454,515996,-748441,1095572,-1581482,2303163,-3375550,4903684,-7149365,10417010,-15111622

%N L.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k) = Sum_{n>=1} a(n)*x^n/n.

%e L.g.f.: L(x) = 2*x + 2*x^2/2 + 5*x^3/3 + 2*x^4/4 + 12*x^5/5 - 13*x^6/6 + 16*x^7/7 - 30*x^8/8 + 41*x^9/9 - 18*x^10/10 + ...

%e exp(L(x)) = 1 + 2*x + 3*x^2 + 5*x^3 + 7*x^4 + 11*x^5 + 13*x^6 + 17*x^7 + 19*x^8 + 23*x^9 + 29*x^10 + ... + A000040(n)*x^n + ...

%t nmax = 44; Rest[CoefficientList[Series[Log[1 + Sum[Prime[k] x^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

%Y Cf. A000040, A007446, A007447, A008578, A030017, A030018, A302194.

%K sign

%O 1,1

%A _Ilya Gutkovskiy_, Apr 18 2018