A092991 Least product of the parts of the partitions of n where that product has the maximum number of divisors.

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

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. Adams-Watters, Jun 14 2006

Links

Amiram Eldar, Table of n, a(n) for n = 0..87

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.

Mathematica

a[n_] := Module[{t = Transpose[{t = Times @@@ IntegerPartitions[n], DivisorSigma[0, t]}]}, MaximalBy[SortBy[t, Last], Last, 1][[1, 1]]]; Array[a, 50, 0] (* Amiram Eldar, Apr 13 2024 *)

Crossrefs

Cf. A092990.

Cf. A000005, A118851.

Sequence in context: A280366 A000784 A355573 * A355649 A102425 A162608

Adjacent sequences: A092988 A092989 A092990 * A092992 A092993 A092994

Keyword

nonn,changed

Author

Amarnath Murthy, Mar 28 2004

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jun 14 2006

Status

approved