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%I #4 Jan 20 2024 09:33:50
%S 1,0,0,0,1,0,1,0,1,5,7,9,12,16,21,28,165,241,354,518,760,1113,1632,
%T 2391,3505,14823,22741,34888,53524,82114,125976,193267,296502,454881,
%U 697859,1070626,1642509,2519868,3865875,5930862,9098878,13959114,21415483,32854729,50404337,77328204
%N Number of compositions (ordered partitions) of n into prime power parts (not including 1) not greater than sqrt(n).
%t Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 45}]
%Y Cf. A280195, A364526.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Jan 16 2024
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