

A326673


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


13



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
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OFFSET

1,2


LINKS



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.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



