A341138 Number of ways to write n as an ordered sum of 9 prime powers (including 1).

1, 9, 45, 165, 495, 1278, 2931, 6111, 11790, 21331, 36594, 60057, 94938, 145296, 216153, 313524, 444483, 617229, 841225, 1127187, 1487322, 1935252, 2486124, 3156408, 3964218, 4928841, 6071472, 7414669, 8983179, 10802970, 12902661, 15311277, 18061092, 21185103, 24720552

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..10000

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, 9):
seq(a(n), n=9..43);  # Alois P. Heinz, Feb 05 2021

Mathematica

nmax = 43; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341127, A341133, A341134, A341135, A341136, A341137, A341139.

Sequence in context: A126899 A162602 A247609 * A008501 A341206 A306942

Adjacent sequences: A341135 A341136 A341137 * A341139 A341140 A341141

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved