

A092991


Least product of the parts of the partitions of n where that product has the maximum number of divisors.


1



1, 1, 2, 2, 4, 6, 6, 12, 12, 24, 36, 48, 60, 60, 120, 180, 240, 360, 360, 720, 1080, 1440, 2160, 2880, 2520, 6480, 5040, 7560, 10080, 15120, 20160, 30240, 45360, 60480, 75600, 120960, 151200, 226800, 302400, 453600, 604800, 907200, 1209600, 1814400
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OFFSET

0,3


COMMENTS

Let P be the set of all products of partitions of n and t = max_{m in P} tau(m). Then a(n) = min_{m in P and tau(m) = t} m. Note that the sequence is not monotonic; the first decrease is a(26) = 5040 < 6480 = a(25) and the second is a(49) = 3326400 < 10886400 = a(48).  Franklin T. AdamsWatters, Jun 14 2006


LINKS

Table of n, a(n) for n=0..43.


EXAMPLE

a(9) = 24 corresponding to the partition (2,2,2,3).
a(8) = 12 corresponding to the partition (1,3,4). Another partition (3,3,2)gives a product 18 with same number of divisors 6 but 18>12 hence a(8) = 12.


CROSSREFS

Cf. A092990.
Cf. A000005, A118851.
Sequence in context: A065457 A280366 A000784 * A102425 A162608 A143216
Adjacent sequences: A092988 A092989 A092990 * A092992 A092993 A092994


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Mar 28 2004


EXTENSIONS

Corrected and extended by Franklin T. AdamsWatters, Jun 14 2006


STATUS

approved



