This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343650 #12 Apr 25 2021 15:14:36
%S A343650 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,
%T A343650 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,
%U A343650 6,2,4,2,8,2,4,2,6,2,4,2,10,2,4,2,6,4,4
%N 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.
%C A343650 See A343651 for the corresponding divisors.
%H A343650 Rémy Sigrist, <a href="/A343650/b343650.txt">Table of n, a(n) for n = 1..10000</a>
%H A343650 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A343650 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F A343650 a(n) <= A000005(n).
%F A343650 a(2^n) = n + 1 for any n >= 0.
%F A343650 a(2^n - 1) = A067824(n) for any n > 0.
%F A343650 A001511(n) divides a(n).
%e A343650 For n = 18:
%e A343650 - we have the following divisors:
%e A343650 d 18/d bin(d) bin(18/d) Requires carries?
%e A343650 -- ---- ------ --------- -----------------
%e A343650 1 18 1 10010 No
%e A343650 2 9 10 1001 No
%e A343650 3 6 11 110 Yes
%e A343650 6 3 110 11 Yes
%e A343650 9 2 1001 10 No
%e A343650 18 1 10010 1 No
%e A343650 - so a(18) = #{1, 2, 9, 18} = 4.
%o A343650 (PARI) a(n, h=hammingweight) = my (hn=h(n)); sumdiv(n, d, hn==h(d)*h(n/d))
%Y A343650 Cf. A000005, A001511, A067824, A266195, A343651.
%K A343650 nonn,base
%O A343650 1,2
%A A343650 _Rémy Sigrist_, Apr 24 2021