A326672 The positions of ones in the binary expansion of n have integer geometric mean.

1, 2, 4, 8, 9, 13, 16, 18, 26, 32, 36, 52, 64, 72, 104, 128, 144, 208, 256, 257, 288, 321, 416, 512, 514, 576, 642, 832, 1024, 1028, 1152, 1284, 1664, 2048, 2056, 2304, 2568, 3328, 4096, 4112, 4608, 5136, 6656, 8192, 8224, 9216, 10272, 13312, 16384, 16448

Offset: 1

Author

Gus Wiseman, Jul 17 2019

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500
• Wikipedia, Geometric mean.

Crossrefs

Partitions with integer geometric mean are A067539.

Subsets with integer geometric mean are A326027.

Factorizations with integer geometric mean are A326028.

Numbers whose binary expansion positions have integer mean are A326669.

Numbers whose binary expansion positions are relatively prime are A326674.

Numbers whose reversed binary expansion positions have integer geometric mean are A326673.

Cf. A000120, A051293, A070939, A291166, A326625.

Programs

Mathematica

Select[Range[100],IntegerQ[GeometricMean[Join@@Position[IntegerDigits[#,2],1]]]&]