login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271716 Sum of numbers of divisors of positive numbers differing from n in one bit. 1

%I

%S 0,2,3,6,6,7,8,13,9,12,13,13,15,18,10,22,15,17,16,22,14,26,14,22,19,

%T 30,13,30,17,20,20,35,18,30,20,27,27,33,18,34,27,26,20,45,16,28,26,34,

%U 26,36,21,47,21,28,26,46,20,32,24,32,32,42,16,52,23,33

%N Sum of numbers of divisors of positive numbers differing from n in one bit.

%C For all the positive numbers m obtained from n by flipping one bit of the binary representation of n, add the number of divisors A000005(m) of m.

%C Number of ordered pairs (a,b) of positive numbers such that a*b differs from n in exactly one binary digit, with no more binary digits than n.

%H Robert Israel, <a href="/A271716/b271716.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 5, flipping one bit yields (4, 7, 1), so a(5) = A000005(4) + A000005(7) + A000005(1) = 3 + 2 + 1 = 6.

%p f:= proc(x)

%p local m;

%p add(numtheory:-tau(m),m=[seq(Bits:-Xor(x,2^j),j=0..ilog2(x))])

%p end proc:

%p map(f, [$1..100]);

%Y Cf. A000005.

%K nonn

%O 1,2

%A _Robert Israel_, Apr 12 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)