A341138 - OEIS

%I #8 Feb 05 2021 21:09:33

%S 1,9,45,165,495,1278,2931,6111,11790,21331,36594,60057,94938,145296,

%T 216153,313524,444483,617229,841225,1127187,1487322,1935252,2486124,

%U 3156408,3964218,4928841,6071472,7414669,8983179,10802970,12902661,15311277,18061092,21185103,24720552

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

%H Alois P. Heinz, <a href="/A341138/b341138.txt">Table of n, a(n) for n = 9..10000</a>

%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, 9):

%p seq(a(n), n=9..43);  # _Alois P. Heinz_, Feb 05 2021

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

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

%K nonn

%O 9,2

%A _Ilya Gutkovskiy_, Feb 05 2021