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

8,2

Links

Table of n, a(n) for n=8..44.

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] &

Crossrefs

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

Sequence in context: A381794 A162596 A331999 * A051192 A008500 A306941

Adjacent sequences: A341134 A341135 A341136 * A341138 A341139 A341140

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved