A213952 Consider the partitions of n in reverse lexicographic ordering (A080577), a(n) is the position of the partition of n which has the maximum LCM. See A000793.

1, 1, 1, 1, 3, 1, 5, 5, 8, 15, 13, 33, 49, 35, 49, 73, 107, 143, 211, 293, 398, 505, 510, 685, 710, 948, 740, 994, 2033, 1735, 2266, 1780, 2333, 4653, 5923, 7311, 9213, 7683, 9719, 17878, 14703, 19072, 22814, 28266, 34878, 42876, 52390

Offset: 1

Author

Robert G. Wilson v, Jul 04 2012

Keywords

• nonn

Comments

As n grows, a(n)/P(n) -> ~1/3, where P(n) is A000041(n).

Examples

			a(5) = 3 because of the seven partitions of 5, {{5}, {4, 1}, {3, 2}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}}; the LCMs of each are: {5, 4, 6, 3, 2, 2, 1}. The third one is the maximum.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..84

Crossrefs

Cf. A000793, A080577, A000041.

Programs

Mathematica

f[n_] := Block[{lst = Apply[LCM, IntegerPartitions@ n, 1]}, Flatten[ Position[ lst, Max@ lst, 1, 1], 1][[1]]]; Array[f, 47]