A098238 Number of ordered ways of writing n as sum of three primes.

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, 15, 30, 12, 30, 18, 37, 12, 39, 21, 42, 24, 46, 9, 51, 18, 48, 24, 54, 18, 66, 21, 60, 30, 67, 24, 81, 18, 75, 30, 79, 18, 87, 21, 87, 36, 93, 15, 105, 30, 105, 36, 97, 12, 120, 30, 114, 36

Offset: 0

Author

Ralf Stephan, Aug 31 2004

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 213. [?Broken link]
• P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 213.

Crossrefs

Cf. A073610, A014612.

Cf. A068307.

Programs

Maple

t1:=add(q^ithprime(n),n=1..1000): series(t1^3,q,1001): seriestolist(%); # N. J. A. Sloane, Sep 29 2006

Mathematica

nn = 74; a = Sum[x^p, {p, Prime[Range[nn]]}]; CoefficientList[Series[a^3, {x, 0, nn}], x] (* Geoffrey Critzer, Jan 25 2015 *)

Formula

G.f.: (Sum_{k>0} x^prime(k))^3. - Vladeta Jovovic, Mar 12 2005

Third convolution of "a(n)=1 if n prime, 0 otherwise" (A010051) with itself. - Graeme McRae, Jul 18 2006