A339452 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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