A303073 L.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k) = Sum_{n>=1} a(n)*x^n/n.

2, 2, 5, 2, 12, -13, 16, -30, 41, -18, 46, -73, 132, -278, 315, -318, 580, -805, 1218, -1998, 2665, -3958, 5936, -7761, 11612, -17678, 25313, -38134, 54754, -76833, 114392, -166334, 240685, -356454, 515996, -748441, 1095572, -1581482, 2303163, -3375550, 4903684, -7149365, 10417010, -15111622

Offset: 1

Author

Ilya Gutkovskiy, Apr 18 2018

Keywords

• sign

Examples

			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 + ...
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 + ...
		

Crossrefs

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

Programs

Mathematica

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