A340964 Number of ways to write n as an ordered sum of 8 primes.

1, 8, 28, 64, 126, 232, 392, 624, 925, 1296, 1800, 2416, 3158, 4088, 5152, 6504, 8142, 9976, 12216, 14784, 17738, 21296, 25272, 29736, 35023, 40768, 47328, 54832, 62728, 71744, 81796, 92736, 105078, 118664, 132924, 149424, 167002, 186144, 206852, 229272, 253023

Offset: 16

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 16..10000

Crossrefs

Column k=8 of A121303.

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

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, 8):
seq(a(n), n=16..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

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

Formula

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