%I #6 Feb 05 2021 18:54:33
%S 1,7,28,84,210,455,882,1569,2611,4116,6223,9093,12901,17822,24053,
%T 31759,41132,52367,65702,81326,99526,120471,144417,171493,201985,
%U 235963,273889,315805,362181,413021,468888,529466,595770,667541,745899,830473,922866,1021832,1129499
%N Number of ways to write n as an ordered sum of 7 prime powers (including 1).
%p q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p b:= proc(n, t) option remember;
%p `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p `if`(q(j), b(n-j, t-1), 0), j=1..n)))
%p end:
%p a:= n-> b(n, 7):
%p seq(a(n), n=7..45); # _Alois P. Heinz_, Feb 05 2021
%t nmax = 45; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y Cf. A000961, A010055, A282062, A282064, A341125, A341133, A341134, A341135, A341137, A341138, A341139.
%K nonn
%O 7,2
%A _Ilya Gutkovskiy_, Feb 05 2021