A340964 - OEIS

%I #10 Mar 18 2022 18:39:22

%S 1,8,28,64,126,232,392,624,925,1296,1800,2416,3158,4088,5152,6504,

%T 8142,9976,12216,14784,17738,21296,25272,29736,35023,40768,47328,

%U 54832,62728,71744,81796,92736,105078,118664,132924,149424,167002,186144,206852,229272,253023

%N Number of ways to write n as an ordered sum of 8 primes.

%H Seiichi Manyama, <a href="/A340964/b340964.txt">Table of n, a(n) for n = 16..10000</a>

%F G.f.: (Sum_{k>=1} x^prime(k))^8.

%p b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;

%p       if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else

%p       while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi

%p     end:

%p a:= n-> b(n, 8):

%p seq(a(n), n=16..56);  # _Alois P. Heinz_, Jan 31 2021

%t nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 16] &

%Y Column k=8 of A121303.

%Y Cf. A000040, A010051, A073610, A098238, A259198, A340960, A340961, A340962, A340963, A340965, A340966.

%K nonn

%O 16,2

%A _Ilya Gutkovskiy_, Jan 31 2021