A092990 -id:A092990 - cp's OEIS frontend

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

Amarnath Murthy, Mar 28 2004

nonn

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

All terms are in A025487. - David A. Corneth, Apr 30 2024

			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.

David A. Corneth, Table of n, a(n) for n = 0..945 (first 88 terms from Amiram Eldar)

Cf. A092990.

Cf. A000005, A025487, A118851.

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 *)

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

cp's OEIS Frontend

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

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