A340966 Number of ways to write n as an ordered sum of 10 primes.

1, 10, 45, 130, 300, 622, 1185, 2100, 3495, 5480, 8266, 12100, 17140, 23730, 32155, 42802, 56400, 73180, 93820, 119250, 149872, 187090, 231765, 284490, 347335, 421332, 507580, 608840, 725500, 859450, 1014473, 1190700, 1392100, 1621710, 1879950, 2172610, 2503580

Offset: 20

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 20..10000

Crossrefs

Column k=10 of A121303.

Cf. A000040, A010051, A073610, A098238, A259201, A340960, A340961, A340962, A340963, A340964, A340965.

Programs

Maple

b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
      if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
      while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
    end:
a:= n-> b(n, 10):
seq(a(n), n=20..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 20] &

Formula

G.f.: (Sum_{k>=1} x^prime(k))^10.