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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

(list; graph; refs; listen; history; text; internal format)

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