|
%I #15 Mar 01 2020 04:36:33
%S 0,2,4,3,34,2,874,25,727,20,4037914,23,522956314,620,35382,40321,
%T 22324392524314,715,6780385526348314,39623,439408062,3301820,
%U 1177652997443428940314,40297,2432903315854636921,442386620,6402373706090881,475412423
%N Integral of exp(-x)*Phi_n(x) from 0 to infinity, Phi_n the n-th cyclotomic polynomial
%C Appears to be all positive integers for n>1, suggesting the possibility of a combinatorial interpretation.
%H Jair Taylor, <a href="/A182103/b182103.txt">Table of n, a(n) for n = 1..497</a>
%t Table[Integrate[Cyclotomic[n, x]/Exp[x], {x, 0, Infinity}], {n, 1, 20}] (* _Vaclav Kotesovec_, Mar 01 2020 *)
%o (Sage)
%o for n in range(1, 40):
%o print(integral(e^(-x)*cyclotomic_polynomial(n),x,0,infinity))
%Y Agrees with A003422(p) for p prime.
%K nonn
%O 1,2
%A _Jair Taylor_, Apr 11 2012
|
