cp's OEIS Frontend

A271984 Numbers n such that the denominator of the sum of the reciprocals of the exponents in the binary expansion of 2n is not equal to their LCM. That is, A271410(n) != A116417(n).

%I A271984 #20 Mar 13 2018 04:37:48
%S A271984 34,35,36,37,38,39,44,45,46,47,50,51,52,53,54,55,60,61,62,63,98,99,
%T A271984 100,101,102,103,108,109,110,111,114,115,116,117,118,119,124,125,126,
%U A271984 127,164,165,166,167,172,173,174,175,180,181,182,183,188,189,190,191
%N A271984 Numbers n such that the denominator of the sum of the reciprocals of the exponents in the binary expansion of 2n is not equal to their LCM. That is, A271410(n) != A116417(n).
%C A271984 a(2*n) = 1 + a(2*n-1) for all n > 0.
%H A271984 Peter Kagey, <a href="/A271984/b271984.txt">Table of n, a(n) for n = 1..10000</a>
%e A271984 a(1) = 34 because 34*2 = 68 is the first number such that the LCM of the exponents in its binary expansion (2 and 6) is unequal to the denominator of the sum of reciprocals: lcm(2, 6) = 6 != denominator(1/2 + 1/6) = 3.
%e A271984 Equivalently, A271410(34) = 6 != A116417(34) = 3.
%t A271984 Select[Range@ 1000, (LCM @@ # != Denominator[ Total[1/#]]) &@ Flatten@ Position[ Reverse@ IntegerDigits[#, 2], 1] &] (* _Giovanni Resta_, Apr 18 2016 *)
%Y A271984 Cf. A116417, A271410.
%K A271984 nonn,base,easy
%O A271984 1,1
%A A271984 _Peter Kagey_, Apr 17 2016