

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



1, 2, 14, 62, 65, 77, 254, 322, 323, 327, 331, 332, 1022, 1281, 1341, 1348, 1349, 1350, 1352, 1353, 1354, 4094, 16382, 21505, 21757, 21762, 21820, 65534, 87299, 87355, 262142, 348161, 349181, 1048574, 1397762, 1398012, 1398020, 1398074, 4194302
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OFFSET

1,2


COMMENTS

All numbers of the form 4^k2, with k>0, appear in this sequence.  Paul Tek, Sep 24 2013


LINKS



FORMULA

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


EXAMPLE

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.


MATHEMATICA

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}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



