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

%I A326673 #17 Sep 30 2019 12:15:08
%S A326673 1,2,4,8,9,11,16,32,64,128,130,138,256,257,261,264,296,388,420,512,
%T A326673 1024,2048,2052,2084,2306,2316,2338,2348,4096,8192,16384,32768,32769,
%U A326673 32776,32777,32899,32904,32907,33024,35072,65536,131072,131074,131084,131106
%N A326673 The positions of ones in the reversed binary expansion of n have integer geometric mean.
%H A326673 Andrew Howroyd, <a href="/A326673/b326673.txt">Table of n, a(n) for n = 1..211</a>
%H A326673 Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>
%e A326673 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.
%t A326673 Select[Range[1000],IntegerQ[GeometricMean[Join@@Position[Reverse[IntegerDigits[#,2]],1]]]&]
%o A326673 (PARI) ok(n)={ispower(prod(i=0, logint(n,2), if(bittest(n,i), i+1, 1)), hammingweight(n))}
%o A326673 { for(n=1, 10^7, if(ok(n), print1(n, ", "))) } \\ _Andrew Howroyd_, Sep 29 2019
%Y A326673 Partitions with integer geometric mean are A067539.
%Y A326673 Subsets with integer geometric mean are A326027.
%Y A326673 Factorizations with integer geometric mean are A326028.
%Y A326673 Numbers whose binary digit positions have integer mean are A326669.
%Y A326673 Numbers whose binary digit positions are relatively prime are A326674.
%Y A326673 Numbers whose binary digit positions have integer geometric mean are A326672.
%Y A326673 Cf. A000120, A051293, A070939, A291166, A326625.
%K A326673 nonn,base
%O A326673 1,2
%A A326673 _Gus Wiseman_, Jul 17 2019