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A358911
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Number of integer compositions of n whose parts all have the same number of prime factors, counted with multiplicity.
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8
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1, 1, 2, 2, 3, 4, 4, 7, 9, 12, 20, 21, 39, 49, 79, 109, 161, 236, 345, 512, 752, 1092, 1628, 2376, 3537, 5171, 7650, 11266, 16634, 24537, 36173, 53377, 78791, 116224, 171598, 253109, 373715, 551434, 814066, 1201466, 1773425, 2617744, 3864050, 5703840, 8419699
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(1) = 1 through a(8) = 9 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (23) (33) (25) (35)
(1111) (32) (222) (52) (44)
(11111) (111111) (223) (53)
(232) (233)
(322) (323)
(1111111) (332)
(2222)
(11111111)
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MAPLE
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b:= proc(n, i) option remember; uses numtheory; `if`(n=0, 1, add(
(t-> `if`(i<0 or i=t, b(n-j, t), 0))(bigomega(j)), j=1..n))
end:
a:= n-> b(n, -1):
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MATHEMATICA
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Table[Length[Select[Join @@ Permutations/@IntegerPartitions[n], SameQ@@PrimeOmega/@#&]], {n, 0, 10}]
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CROSSREFS
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For sequences of partitions see A358905.
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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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