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A340961 Number of ways to write n as an ordered sum of 5 primes.

%I A340961 #10 Mar 18 2022 18:39:03
%S A340961 1,5,10,15,25,36,50,65,70,90,110,125,155,170,200,241,270,300,350,375,
%T A340961 435,500,530,600,640,696,760,850,840,985,990,1170,1160,1370,1250,1570,
%U A340961 1445,1760,1600,2000,1710,2340,1950,2555,2165,2876,2320,3340,2560,3595,2880,3985,3050
%N A340961 Number of ways to write n as an ordered sum of 5 primes.
%H A340961 Seiichi Manyama, <a href="/A340961/b340961.txt">Table of n, a(n) for n = 10..10000</a>
%F A340961 G.f.: (Sum_{k>=1} x^prime(k))^5.
%p A340961 b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
%p A340961       if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
%p A340961       while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
%p A340961     end:
%p A340961 a:= n-> b(n, 5):
%p A340961 seq(a(n), n=10..62);  # _Alois P. Heinz_, Jan 31 2021
%t A340961 nmax = 62; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 10] &
%Y A340961 Column k=5 of A121303.
%Y A340961 Cf. A000040, A010051, A073610, A098238, A259195, A340960, A340962, A340963, A340964, A340965, A340966.
%K A340961 nonn
%O A340961 10,2
%A A340961 _Ilya Gutkovskiy_, Jan 31 2021