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 A280195 Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221). 10
 1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287596, 455647, 721847, 1143588, 1811748, 2870239, 4547232, 7203907, 11412882, 18080833, 28644680, 45380392, 71894054, 113898439, 180443915, 285869028, 452888824, 717490903, 1136687237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Number of compositions (ordered partitions) into prime powers (1 excluded). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Prime Power FORMULA G.f.: 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k). EXAMPLE a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2]. MATHEMATICA nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x] CROSSREFS Cf. A001221, A023360, A023894, A246655. Sequence in context: A135909 A046812 A269797 * A286224 A245388 A164573 Adjacent sequences:  A280192 A280193 A280194 * A280196 A280197 A280198 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 28 2016 STATUS approved

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Last modified August 12 11:44 EDT 2020. Contains 336439 sequences. (Running on oeis4.)