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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
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
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
KEYWORD
nonn
AUTHOR
Robert Israel, Apr 12 2016
STATUS
approved