

A098238


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


10



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
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OFFSET

0,8


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.


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


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 *)


CROSSREFS

Cf. A073610, A014612.
Cf. A068307
Sequence in context: A130481 A145805 A277192 * A088651 A161019 A137901
Adjacent sequences: A098235 A098236 A098237 * A098239 A098240 A098241


KEYWORD

nonn


AUTHOR

Ralf Stephan, Aug 31 2004


STATUS

approved



