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%I #5 Jan 20 2024 09:33:12
%S 1,1,1,1,3,3,4,4,5,12,14,16,19,21,24,27,64,72,84,94,108,120,136,150,
%T 169,377,427,480,540,603,674,748,831,918,1014,1115,1226,1342,1469,
%U 1602,1747,1898,2062,2233,2418,2611,2818,3034,3266,7529,8185,8884,9632,10427,11276,12177
%N Number of partitions of n into prime power parts (including 1) not greater than sqrt(n).
%t Table[SeriesCoefficient[Product[1/(1 - Boole[k == 1 || PrimePowerQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 55}]
%Y Cf. A023893, A097356, A369219.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Jan 16 2024
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