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A095376 Values of n such that the total number of 1's in the binary expansions of the first n integers is a multiple of n. 5

%I

%S 1,2,14,62,65,77,254,322,323,327,331,332,1022,1281,1341,1348,1349,

%T 1350,1352,1353,1354,4094,16382,21505,21757,21762,21820,65534,87299,

%U 87355,262142,348161,349181,1048574,1397762,1398012,1398020,1398074,4194302

%N Values of n such that the total number of 1's in the binary expansions of the first n integers is a multiple of n.

%C All numbers of the form 4^k-2, with k>0, appear in this sequence. - _Paul Tek_, Sep 24 2013

%H Donovan Johnson, <a href="/A095376/b095376.txt">Table of n, a(n) for n = 1..100</a>

%F Integer solutions to {A000788(x)/x is integer}.

%e n=14: {1, 10, 11, 10, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110} includes 28 1's so A000788(14)/14 = 2 is integer, thus 14 is here.

%t lib[x_] := Count[IntegerDigits[x, 2], 1]; {s=0, ta=Table[0, {100}], tb=Table[0, {100}], u=1}; Do[s=s+lib[n]; w=n; If[IntegerQ[s/n], Print[{n, s/n}]; ta[[u]]=n; tb[[u]]=s/n; u=u+1], {n, 100000}]

%Y Cf. A000120, A000788, A014499, A095375.

%K nonn

%O 1,2

%A _Labos Elemer_, Jun 07 2004

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Last modified August 13 21:51 EDT 2020. Contains 336450 sequences. (Running on oeis4.)