A340961 - OEIS

%I #10 Mar 18 2022 18:39:03

%S 1,5,10,15,25,36,50,65,70,90,110,125,155,170,200,241,270,300,350,375,

%T 435,500,530,600,640,696,760,850,840,985,990,1170,1160,1370,1250,1570,

%U 1445,1760,1600,2000,1710,2340,1950,2555,2165,2876,2320,3340,2560,3595,2880,3985,3050

%N Number of ways to write n as an ordered sum of 5 primes.

%H Seiichi Manyama, <a href="/A340961/b340961.txt">Table of n, a(n) for n = 10..10000</a>

%F G.f.: (Sum_{k>=1} x^prime(k))^5.

%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, 5):

%p seq(a(n), n=10..62);  # _Alois P. Heinz_, Jan 31 2021

%t nmax = 62; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 10] &

%Y Column k=5 of A121303.

%Y Cf. A000040, A010051, A073610, A098238, A259195, A340960, A340962, A340963, A340964, A340965, A340966.

%K nonn

%O 10,2

%A _Ilya Gutkovskiy_, Jan 31 2021