A326673 - OEIS

%I #17 Sep 30 2019 12:15:08

%S 1,2,4,8,9,11,16,32,64,128,130,138,256,257,261,264,296,388,420,512,

%T 1024,2048,2052,2084,2306,2316,2338,2348,4096,8192,16384,32768,32769,

%U 32776,32777,32899,32904,32907,33024,35072,65536,131072,131074,131084,131106

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

%H Andrew Howroyd, <a href="/A326673/b326673.txt">Table of n, a(n) for n = 1..211</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>

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

%o (PARI) ok(n)={ispower(prod(i=0, logint(n,2), if(bittest(n,i), i+1, 1)), hammingweight(n))}

%o { for(n=1, 10^7, if(ok(n), print1(n, ", "))) } \\ _Andrew Howroyd_, Sep 29 2019

%Y Partitions with integer geometric mean are A067539.

%Y Subsets with integer geometric mean are A326027.

%Y Factorizations with integer geometric mean are A326028.

%Y Numbers whose binary digit positions have integer mean are A326669.

%Y Numbers whose binary digit positions are relatively prime are A326674.

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

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

%K nonn,base

%O 1,2

%A _Gus Wiseman_, Jul 17 2019