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A331022
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Numbers k such that the number of strict integer partitions of k is a power of 2.
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8
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0, 1, 2, 3, 4, 6, 9, 16, 20, 29, 34, 45
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OFFSET
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0,3
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COMMENTS
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An integer partition of n is a finite, nonincreasing sequence of positive integers (parts) summing to n. It is strict if the parts are all different. Integer partitions and strict integer partitions are counted by A000041 and A000009 respectively.
Conjecture: This sequence is finite.
Conjecture: The analogous sequence for non-strict partitions is: 0, 1, 2.
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LINKS
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EXAMPLE
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The strict integer partitions of the initial terms:
(1) (2) (3) (4) (6) (9)
(2,1) (3,1) (4,2) (5,4)
(5,1) (6,3)
(3,2,1) (7,2)
(8,1)
(4,3,2)
(5,3,1)
(6,2,1)
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MATHEMATICA
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Select[Range[0, 1000], IntegerQ[Log[2, PartitionsQ[#]]]&]
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CROSSREFS
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The version for primes instead of powers of 2 is A035359.
The version for factorizations instead of strict partitions is A330977.
Numbers whose number of partitions is prime are A046063.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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