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

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..211

Wikipedia, Geometric mean

Example

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.

Mathematica

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

Prog

(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

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.

Sequence in context: A035271 A338047 A243186 * A297126 A044814 A342009

Adjacent sequences: A326670 A326671 A326672 * A326674 A326675 A326676

Keyword

nonn,base

Author

Gus Wiseman, Jul 17 2019

Status

approved