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A090184
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Number of partitions of the n-th 3-smooth number into parts 2 and 3.
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5
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0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 10, 11, 13, 14, 17, 19, 22, 25, 28, 33, 37, 41, 43, 49, 55, 65, 73, 82, 86, 97, 109, 122, 129, 145, 163, 171, 193, 217, 244, 257, 289, 325, 342, 365, 385, 433, 487, 513, 577, 649, 683, 730, 769, 865, 973, 1025, 1094, 1153
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OFFSET
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1,5
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LINKS
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FORMULA
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a(2^i * 3^j) = floor(2^(i-1) * 3^(j-1) + 1), i*j>0.
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EXAMPLE
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n=11: A003586(11) = 2^3 * 3 = 24: 3+3+3+3+3+3+3+3 = 3+3+3+3+3+3+2+2+2 = 3+3+3+3+2+2+2+2+2+2 = 3+3+2+2+2+2+2+2+2+2+2 = 2+2+2+2+2+2+2+2+2+2+2+2: a(11)=5.
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MATHEMATICA
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smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;
Length[IntegerPartitions[#, All, {2, 3}]]& /@ Select[Range[10000], smooth3Q] (* Jean-François Alcover, Oct 13 2021 *)
With[{nn = 6^5}, Map[Floor[#/2] - Floor[#/3] &, Union@ Flatten@ Table[2^a * 3^b, {a, 0, Log2[#]}, {b, 0, Log[3, #/(2^a)]}] &[nn] + 2]] (* Michael De Vlieger, Oct 13 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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