A339452 Number of compositions (ordered partitions) of n into distinct parts such that the geometric mean of the parts is an integer.

1, 1, 1, 1, 3, 1, 7, 1, 1, 5, 1, 1, 9, 7, 3, 1, 3, 1, 7, 11, 13, 1, 7, 1, 11, 35, 25, 31, 27, 5, 157, 1, 31, 131, 39, 31, 33, 37, 183, 179, 135, 157, 7, 265, 3, 871, 187, 865, 259, 879, 867, 179, 1593, 6073, 1593, 271, 5995, 149, 6661, 2411, 1509, 997, 1045, 5887

Offset

1,5

Links

Table of n, a(n) for n=1..64.

Eric W. Weisstein's World of Mathematics, Geometric Mean

Index entries for sequences related to compositions

Example

a(10) = 5 because we have [10], [9, 1], [1, 9], [8, 2] and [2, 8].

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&IntegerQ[GeometricMean[#]]&]], {n, 0, 15}] (* Gus Wiseman, Oct 30 2022 *)

Crossrefs

For partitions we have A326625, non-strict A067539 (ranked by A326623).

The version for subsets is A326027.

For arithmetic mean we have A339175, non-strict A271654.

The non-strict case is counted by A357710, ranked by A357490.

A032020 counts strict compositions.

A067538 counts partitions with integer average.

A078175 lists numbers whose prime factors have integer average.

A320322 counts partitions whose product is a perfect power.

Cf. A051293, A078174, A096199, A102627, A326622, A326624, A326028, A326641, A326645, A335405.

Sequence in context: A340878 A346182 A026499 * A242114 A143470 A114580

Adjacent sequences: A339449 A339450 A339451 * A339453 A339454 A339455

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved