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 A307314 #23 Feb 08 2025 04:52:19 %S A307314 1,2,1,3,2,3,1,4,2,3,1,5,1,2,1,5,2,5,1,5,2,2,1,7,2,2,2,4,1,3,1,6,2,4, %T A307314 1,7,2,3,1,7,2,4,1,3,2,2,1,9,1,4,2,3,1,4,1,6,1,2,1,6,1,2,1,7,4,6,1,6, %U A307314 2,3,1,10,2,3,1,4,1,3,1,9 %N A307314 Number of divisors d of 2n such that adding d to 2n in binary requires no carries. %C A307314 Equivalently, number of numbers d such that d|2n and d AND 2n = 0. %C A307314 First differences of either bisection of A325123. %H A307314 Amiram Eldar, <a href="/A307314/b307314.txt">Table of n, a(n) for n = 1..10000</a> %F A307314 A001511(n) <= a(n) <= A000005(n). %F A307314 a(p) = 1 + [p is in A247068] for p prime, where [] is the Iverson bracket. %t A307314 a[n_] := DivisorSum[2*n, 1 &, BitAnd[#, 2*n] == 0 &]; Array[a, 100] (* _Amiram Eldar_, Feb 08 2025 *) %o A307314 (PARI) a(n) = sumdiv(2*n, d, bitand(d, 2*n) == 0); \\ _Michel Marcus_, Apr 02 2019 %Y A307314 Cf. A325123, A001511, A000005, A247068. %K A307314 nonn %O A307314 1,2 %A A307314 _Charlie Neder_, Apr 02 2019