A309837 - OEIS

A309837

Where records occur in A327642.

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

1,2

COMMENTS

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?

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

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.

CROSSREFS

Cf. A327642.

Sequence in context: A068354 A354591 A075027 * A310659 A076298 A194579

Adjacent sequences: A309834 A309835 A309836 * A309838 A309839 A309840

KEYWORD

nonn

AUTHOR

David A. Corneth, Sep 22 2019

STATUS

approved