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A316896
Number of aperiodic integer partitions of n whose reciprocal sum is 1.
0
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 3, 5, 5, 2, 2, 5, 5, 9, 3, 4, 6, 4, 3, 6, 8, 4, 10, 9, 8, 11, 7, 13, 12, 15, 15, 21, 18, 16, 21, 19, 17, 30, 23, 19, 23, 28, 25, 29, 34, 29, 44, 28, 46, 48, 42
OFFSET
1,22
COMMENTS
The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
A partition is aperiodic if its multiplicities are relatively prime.
EXAMPLE
The a(37) = 5 partitions are (24,8,3,2), (20,5,4,4,4), (15,10,6,3,3), (14,7,7,7,2), (10,10,10,5,2).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And[GCD@@Length/@Split[#]==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
EXTENSIONS
a(51)-a(80) from Giovanni Resta, Jul 16 2018
STATUS
approved