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%I #6 Jan 15 2024 11:13:51
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,
%T 9,9,37,37,40,40,44,44,48,48,52,52,56,56,61,61,65,65,70,70,75,75,80,
%U 80,85,85,91,91,96,96,351,351,378,378,411,411,441
%N Number of partitions of n into nonprime parts not greater than sqrt(n).
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p b(n, i-1)+`if`(isprime(i), 0, b(n-i, min(n-i, i)))))
%p end:
%p a:= n-> b(n, floor(sqrt(n))):
%p seq(a(n), n=0..70); # _Alois P. Heinz_, Jan 13 2024
%t Table[SeriesCoefficient[Product[1/(1 - Boole[!PrimeQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 70}]
%Y Cf. A002095, A097356.
%K nonn
%O 0,17
%A _Ilya Gutkovskiy_, Jan 08 2024
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