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A316897
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Number of integer partitions of n into relatively prime parts whose reciprocal sum is 1.
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0
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 3, 1, 2, 1, 1, 1, 2, 1, 5, 3, 1, 1, 5, 2, 9, 3, 3, 3, 4, 2, 6, 6, 3, 4, 9, 5, 10, 5, 10, 9, 15, 10, 21, 12, 14, 16, 18, 9, 30, 18, 17, 17, 28, 16, 29, 26, 26, 30, 28, 33, 48, 31
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OFFSET
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1,22
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COMMENTS
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The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
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LINKS
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EXAMPLE
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The a(43) = 9 partitions:
(24,8,4,4,3)
(21,7,7,6,2)
(20,12,5,3,3)
(20,8,8,5,2)
(15,15,6,5,2)
(15,12,10,4,2)
(14,7,7,7,4,4)
(12,8,8,6,6,3)
(10,10,10,5,4,4).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And[GCD@@#==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]
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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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