A340963 Number of ways to write n as an ordered sum of 7 primes.

1, 7, 21, 42, 77, 133, 210, 316, 434, 574, 770, 980, 1239, 1547, 1876, 2331, 2828, 3367, 4032, 4746, 5565, 6574, 7602, 8757, 10136, 11480, 13132, 14882, 16646, 18662, 20951, 23268, 26082, 28861, 31787, 35218, 38745, 42532, 46403, 50883, 54810, 60613, 65016, 71302, 76069

Offset: 14

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 14..10000

Crossrefs

Column k=7 of A121303.

Cf. A000040, A010051, A073610, A098238, A259197, A340960, A340961, A340962, 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, 7):
seq(a(n), n=14..58);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 58; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 14] &

Formula

G.f.: (Sum_{k>=1} x^prime(k))^7.