login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

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
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, 30, 13, 30, 17, 20, 20, 35, 18, 30, 20, 27, 27, 33, 18, 34, 27, 26, 20, 45, 16, 28, 26, 34, 26, 36, 21, 47, 21, 28, 26, 46, 20, 32, 24, 32, 32, 42, 16, 52, 23, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

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.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MAPLE

f:= proc(x)

  local m;

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

end proc:

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

CROSSREFS

Cf. A000005.

Sequence in context: A193896 A099162 A187327 * A220178 A023832 A080235

Adjacent sequences:  A271713 A271714 A271715 * A271717 A271718 A271719

KEYWORD

nonn

AUTHOR

Robert Israel, Apr 12 2016

STATUS

approved

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 November 30 13:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)