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A357859
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Number of integer factorizations of 2n into distinct even factors.
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1
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1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 3, 1, 4, 1, 2, 1, 4, 1, 2, 1, 5, 1, 3, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 3, 1, 5, 1, 2, 1, 6, 1, 2, 1, 5, 1, 3, 1, 3, 1, 3, 1, 7, 1, 2, 1, 3, 1, 3, 1, 7, 1, 2, 1, 6, 1, 2, 1
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OFFSET
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1,4
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LINKS
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EXAMPLE
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The a(n) factorizations for n = 2, 4, 12, 24, 32, 48, 60, 96:
(4) (8) (24) (48) (64) (96) (120) (192)
(2*4) (4*6) (6*8) (2*32) (2*48) (2*60) (2*96)
(2*12) (2*24) (4*16) (4*24) (4*30) (4*48)
(4*12) (2*4*8) (6*16) (6*20) (6*32)
(2*4*6) (8*12) (10*12) (8*24)
(2*6*8) (2*6*10) (12*16)
(2*4*12) (4*6*8)
(2*4*24)
(2*6*16)
(2*8*12)
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MATHEMATICA
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facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[2*n], UnsameQ@@#&&OddQ[Times@@(#+1)]&]], {n, 100}]
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CROSSREFS
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The version for partitions instead of factorizations is A000009.
A001222 counts prime-power divisors.
A050361 counts strict factorizations into prime powers.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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