A271716 Sum of numbers of divisors of positive numbers differing from n in one bit.

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

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 * A362706 A220178 A023832

Adjacent sequences: A271713 A271714 A271715 * A271717 A271718 A271719

Keyword

nonn

Author

Robert Israel, Apr 12 2016

Status

approved