A341136 Number of ways to write n as an ordered sum of 7 prime powers (including 1).

1, 7, 28, 84, 210, 455, 882, 1569, 2611, 4116, 6223, 9093, 12901, 17822, 24053, 31759, 41132, 52367, 65702, 81326, 99526, 120471, 144417, 171493, 201985, 235963, 273889, 315805, 362181, 413021, 468888, 529466, 595770, 667541, 745899, 830473, 922866, 1021832, 1129499

Offset

7,2

Links

Table of n, a(n) for n=7..45.

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, 7):
seq(a(n), n=7..45);  # Alois P. Heinz, Feb 05 2021

Mathematica

nmax = 45; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

Crossrefs

Cf. A000961, A010055, A282062, A282064, A341125, A341133, A341134, A341135, A341137, A341138, A341139.

Sequence in context: A162595 A073363 A247608 * A166322 A008499 A049018

Adjacent sequences: A341133 A341134 A341135 * A341137 A341138 A341139

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved