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