A341133 Number of ways to write n as an ordered sum of 4 prime powers (including 1).

1, 4, 10, 20, 35, 52, 72, 96, 125, 156, 196, 236, 277, 316, 362, 400, 451, 496, 554, 604, 668, 704, 770, 808, 871, 920, 1014, 1040, 1131, 1172, 1266, 1308, 1449, 1484, 1638, 1672, 1802, 1820, 1992, 1964, 2167, 2172, 2332, 2296, 2534, 2444, 2698, 2648, 2889, 2820, 3140

Offset

4,2

Links

Table of n, a(n) for n=4..54.

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, 4):
seq(a(n), n=4..54);  # Alois P. Heinz, Feb 05 2021

Mathematica

nmax = 54; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341122, A341134, A341135, A341136, A341137, A341138, A341139.

Sequence in context: A353128 A362072 A102533 * A008033 A047954 A008144

Adjacent sequences: A341130 A341131 A341132 * A341134 A341135 A341136

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved