A326673 The positions of ones in the reversed binary expansion of n have integer geometric mean.

1, 2, 4, 8, 9, 11, 16, 32, 64, 128, 130, 138, 256, 257, 261, 264, 296, 388, 420, 512, 1024, 2048, 2052, 2084, 2306, 2316, 2338, 2348, 4096, 8192, 16384, 32768, 32769, 32776, 32777, 32899, 32904, 32907, 33024, 35072, 65536, 131072, 131074, 131084, 131106

Offset: 1

Author

Gus Wiseman, Jul 17 2019

Keywords

• nonn
• base

Examples

			The reversed binary expansion of 11 is (1,1,0,1) and {1,2,4} has integer geometric mean, so 11 is in the sequence.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..211
• 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 digit positions have integer mean are A326669.

Numbers whose binary digit positions are relatively prime are A326674.

Numbers whose binary digit positions have integer geometric mean are A326672.

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

Programs

Mathematica

Select[Range[1000],IntegerQ[GeometricMean[Join@@Position[Reverse[IntegerDigits[#,2]],1]]]&]

PARI

ok(n)={ispower(prod(i=0, logint(n,2), if(bittest(n,i), i+1, 1)), hammingweight(n))}
{ for(n=1, 10^7, if(ok(n), print1(n, ", "))) } \\ Andrew Howroyd, Sep 29 2019