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A316897 Number of integer partitions of n into relatively prime parts whose reciprocal sum is 1. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,22
COMMENTS
The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
LINKS
EXAMPLE
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).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And[GCD@@#==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]
CROSSREFS
Sequence in context: A309395 A260943 A316893 * A151756 A112053 A089798
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
EXTENSIONS
a(71)-a(80) from Giovanni Resta, Jul 16 2018
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)