login
A092991
Least product of the parts of the partitions of n where that product has the maximum number of divisors.
2
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
All terms are in A025487. - David A. Corneth, Apr 30 2024
LINKS
David A. Corneth, Table of n, a(n) for n = 0..945 (first 88 terms from Amiram Eldar)
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 28 2004
EXTENSIONS
Corrected and extended by Franklin T. Adams-Watters, Jun 14 2006
STATUS
approved