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A309837
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Where records occur in A327642.
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0
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0, 4, 6, 8, 10, 12, 16, 18, 24, 30, 36, 48, 60, 72, 84, 96, 108, 120, 144, 168, 180, 240, 300, 336, 360, 420, 480, 504, 540, 600, 660, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4320, 4620, 4680, 5040, 6720, 7560, 9240, 10080, 12600, 13860
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OFFSET
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1,2
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COMMENTS
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Numbers where the number of partitions of n into divisors of n that are at most sqrt(n) increases to a record.
Is k unbounded where k | a(n) for all n > m for some m. For example, does 2 | a(n) for all n > 1? Does 60 | a(n) for all n > 27?
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LINKS
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EXAMPLE
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There are 1072 partitions of 36 into divisors <= sqrt(36) of 36, i.e. there are 1072 partitions of 36 into parts 1, 2, 3 and 6. For all k < 36, this number of partitions is < 1073 so 36 is in the sequence.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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