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

1,5

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000793, A080577, A000041.

Sequence in context: A186754 A124741 A339419 * A205873 A220479 A146913

Adjacent sequences: A213949 A213950 A213951 * A213953 A213954 A213955

Keyword

nonn

Author

Robert G. Wilson v, Jul 04 2012

Status

approved