A341137 Number of ways to write n as an ordered sum of 8 prime powers (including 1).

1, 8, 36, 120, 330, 784, 1660, 3208, 5763, 9752, 15724, 24368, 36520, 53152, 75392, 104464, 141717, 188624, 246836, 318088, 404356, 507656, 630172, 774048, 941685, 1135304, 1357652, 1611240, 1899138, 2224016, 2589352, 2997544, 3452619, 3957480, 4516912, 5134096, 5815338

Offset: 8

Author

Ilya Gutkovskiy, Feb 05 2021

Keywords

• nonn

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341126, A341133, A341134, A341135, A341136, A341138, A341139.

Programs

Maple

q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(q(j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..44);  # Alois P. Heinz, Feb 05 2021

Mathematica

nmax = 44; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &