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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
OFFSET
1,2
LINKS
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.
Sequence in context: A035271 A338047 A243186 * A297126 A044814 A342009
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved