cp's OEIS Frontend

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

%I A341133 #6 Feb 05 2021 18:41:53
%S A341133 1,4,10,20,35,52,72,96,125,156,196,236,277,316,362,400,451,496,554,
%T A341133 604,668,704,770,808,871,920,1014,1040,1131,1172,1266,1308,1449,1484,
%U A341133 1638,1672,1802,1820,1992,1964,2167,2172,2332,2296,2534,2444,2698,2648,2889,2820,3140
%N A341133 Number of ways to write n as an ordered sum of 4 prime powers (including 1).
%p A341133 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341133 b:= proc(n, t) option remember;
%p A341133       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341133       `if`(q(j), b(n-j, t-1), 0), j=1..n)))
%p A341133     end:
%p A341133 a:= n-> b(n, 4):
%p A341133 seq(a(n), n=4..54);  # _Alois P. Heinz_, Feb 05 2021
%t A341133 nmax = 54; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A341133 Cf. A000961, A010055, A282062, A282064, A341122, A341134, A341135, A341136, A341137, A341138, A341139.
%K A341133 nonn
%O A341133 4,2
%A A341133 _Ilya Gutkovskiy_, Feb 05 2021