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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 Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904. Sequence in context: A309395 A260943 A316893 * A151756 A112053 A089798 Adjacent sequences:  A316894 A316895 A316896 * A316898 A316899 A316900 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 April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)