A341134 Number of ways to write n as an ordered sum of 5 prime powers (including 1).

1, 5, 15, 35, 70, 121, 190, 280, 395, 535, 711, 920, 1160, 1425, 1725, 2041, 2395, 2775, 3200, 3645, 4146, 4640, 5190, 5730, 6325, 6915, 7625, 8270, 9030, 9745, 10576, 11320, 12320, 13185, 14305, 15281, 16510, 17480, 18855, 19835, 21306, 22435, 24010, 25025, 26810, 27790, 29590

Offset

5,2

Links

Table of n, a(n) for n=5..51.

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, 5):
seq(a(n), n=5..51);  # Alois P. Heinz, Feb 05 2021

Mathematica

nmax = 51; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341123, A341133, A341135, A341136, A341137, A341138, A341139.

Sequence in context: A005894 A015622 A346761 * A292103 A290447 A360051

Adjacent sequences: A341131 A341132 A341133 * A341135 A341136 A341137

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved