A272035 - OEIS

%I #20 Apr 30 2016 19:49:15

%S 0,1,38,39,2090,2091,16902,16903,18954,18955,18988,18989,131334,

%T 131335,133386,133387,133420,133421,148258,148259,150284,150285,

%U 524314,524315,524348,524349,526386,526387,541212,541213,543250,543251,543284,543285,655644,655645,657682

%N Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.

%C That is, numbers such that A116416(n) equals 1.

%C 2k is in this sequence if and only if 2k + 1 is. Therefore n + a(n) is odd for all n. - _Peter Kagey_, Apr 19 2016

%H Peter Kagey, <a href="/A272035/b272035.txt">Table of n, a(n) for n = 1..450</a> (All terms less than 2^30)

%e For n=39, 39_10=100111_2, and 1/1 + 1/2 + 1/3 + 1/6 = 2, an integer.

%t Select[Range[2^20], IntegerQ@ Total[1/Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &] (* _Michael De Vlieger_, Apr 18 2016 *)

%o (PARI) isok(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k)) == 1;}

%Y Cf. A116416, A116417, A272034, A272036, A272082.

%K nonn

%O 1,3

%A _Michel Marcus_, Apr 18 2016