A343650 a(n) is the number of divisors d of n such that the product d * (n/d) can be computed without carries in binary.
1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 4, 5, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 4, 6, 2, 8, 2, 6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 4, 4, 2, 10, 2, 4, 4, 6, 2, 8, 2, 8, 2, 4, 2, 12, 2, 4, 6, 7, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 6, 4, 4
Offset: 1
Examples
For n = 18:
- we have the following divisors:
d 18/d bin(d) bin(18/d) Requires carries?
-- ---- ------ --------- -----------------
1 18 1 10010 No
2 9 10 1001 No
3 6 11 110 Yes
6 3 110 11 Yes
9 2 1001 10 No
18 1 10010 1 No
- so a(18) = #{1, 2, 9, 18} = 4.
Links
Programs
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PARI
a(n, h=hammingweight) = my (hn=h(n)); sumdiv(n, d, hn==h(d)*h(n/d))
Comments