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%I #6 Jan 15 2024 11:14:27
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,95,131,181,250,345,476,657,907,1252,
%T 1728,2385,3292,4544,6272,8657,11949,16493,22765,31422,43371,439373,
%U 643932,943728,1383100,2027032,2970760,4353861,6380893,9351653,13705513,20086406,29438059
%N Number of compositions (ordered partitions) of n into nonprime parts not greater than sqrt(n).
%p b:= proc(n, t) option remember; `if`(n=0, 1, add(
%p `if`(isprime(j), 0, b(n-j, t)), j=1..min(n, t)))
%p end:
%p a:= n-> b(n, floor(sqrt(n))):
%p seq(a(n), n=0..47); # _Alois P. Heinz_, Jan 13 2024
%t Table[SeriesCoefficient[1/(1 - Sum[Boole[!PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]
%Y Cf. A052284, A364526.
%K nonn
%O 0,17
%A _Ilya Gutkovskiy_, Jan 08 2024