cp's OEIS Frontend

A272035 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.

%I A272035 #20 Apr 30 2016 19:49:15
%S A272035 0,1,38,39,2090,2091,16902,16903,18954,18955,18988,18989,131334,
%T A272035 131335,133386,133387,133420,133421,148258,148259,150284,150285,
%U A272035 524314,524315,524348,524349,526386,526387,541212,541213,543250,543251,543284,543285,655644,655645,657682
%N A272035 Numbers n such that the sum of the inverse of the exponents in the binary expansion of 2n is an integer.
%C A272035 That is, numbers such that A116416(n) equals 1.
%C A272035 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 A272035 Peter Kagey, <a href="/A272035/b272035.txt">Table of n, a(n) for n = 1..450</a> (All terms less than 2^30)
%e A272035 For n=39, 39_10=100111_2, and 1/1 + 1/2 + 1/3 + 1/6 = 2, an integer.
%t A272035 Select[Range[2^20], IntegerQ@ Total[1/Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &] (* _Michael De Vlieger_, Apr 18 2016 *)
%o A272035 (PARI) isok(n) = {my(b = Vecrev(binary(n))); denominator(sum(k=1, #b, b[k]/k)) == 1;}
%Y A272035 Cf. A116416, A116417, A272034, A272036, A272082.
%K A272035 nonn
%O A272035 1,3
%A A272035 _Michel Marcus_, Apr 18 2016