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

Offset: 1

Author

David A. Corneth, Sep 22 2019

Keywords

• nonn

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?

Examples

			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.