|
%I #20 May 03 2019 22:16:41
%S 0,0,0,0,0,0,1,3,3,4,6,6,9,6,6,10,9,12,12,12,12,19,12,21,15,21,18,30,
%T 15,30,12,30,18,37,12,39,21,42,24,46,9,51,18,48,24,54,18,66,21,60,30,
%U 67,24,81,18,75,30,79,18,87,21,87,36,93,15,105,30,105,36,97,12,120,30,114,36
%N Number of ordered ways of writing n as sum of three primes.
%H T. D. Noe, <a href="/A098238/b098238.txt">Table of n, a(n) for n = 0..10000</a>
%H P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">Analytic and Combinatorial Number Theory</a> Course Notes, p. 213. [?Broken link]
%H P. Pollack, <a href="http://alpha01.dm.unito.it/personalpages/cerruti/ac/notes.pdf">Analytic and Combinatorial Number Theory</a> Course Notes, p. 213.
%F G.f.: (Sum_{k>0} x^prime(k))^3. - _Vladeta Jovovic_, Mar 12 2005
%F Third convolution of "a(n)=1 if n prime, 0 otherwise" (A010051) with itself. - _Graeme McRae_, Jul 18 2006
%p t1:=add(q^ithprime(n),n=1..1000): series(t1^3,q,1001): seriestolist(%); # _N. J. A. Sloane_, Sep 29 2006
%t nn = 74; a = Sum[x^p, {p, Prime[Range[nn]]}]; CoefficientList[Series[a^3, {x, 0, nn}], x] (* _Geoffrey Critzer_, Jan 25 2015 *)
%Y Cf. A073610, A014612.
%Y Cf. A068307.
%K nonn
%O 0,8
%A _Ralf Stephan_, Aug 31 2004
|
