A340962 Number of ways to write n as an ordered sum of 6 primes.

1, 6, 15, 26, 45, 72, 106, 150, 186, 236, 306, 366, 455, 540, 636, 782, 912, 1056, 1236, 1410, 1617, 1896, 2106, 2400, 2696, 2976, 3348, 3716, 4026, 4446, 4917, 5340, 5982, 6380, 7017, 7476, 8377, 8640, 9765, 9936, 11202, 11496, 13132, 12930, 15117, 14672, 17178, 16800, 19696

Offset: 12

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 12..10000

Crossrefs

Column k=6 of A121303.

Cf. A000040, A010051, A073610, A098238, A259196, A340960, A340961, A340963, A340964, 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, 6):
seq(a(n), n=12..60);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^6, {x, 0, nmax}], x] // Drop[#, 12] &

Formula

G.f.: (Sum_{k>=1} x^prime(k))^6.