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 A379234 #17 Jan 07 2025 08:46:30
%S A379234 312,428,672,760,5009850
%N A379234 Numbers k for which k XOR 2*k = sigma(k), where sigma is the sum of divisors function.
%C A379234 Equally, numbers k such that 2*k XOR sigma(k) = k, i.e., k XOR sigma(k) = 2*k.
%C A379234 If it exists, a(6) > 2^33.
%H A379234 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A379234 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379234 {k such that A000203(k) = A048724(k)}.
%e A379234 672 has binary expansion 1010100000_2, and 672 XOR 2*672 has binary expansion 11111100000_2 = 2016 (= 63*32) = sigma(672), so 672 is included in this sequence. Notably, as 672 is also a Fibbinary number (in A003714, no adjacent 1-bits), it follows that 672 XOR 2*672 = 3*672, and thus 672 is also a 3-perfect number, A005820.
%o A379234 (PARI) is_A379234(n) = (bitxor(2*n,n)==sigma(n));
%Y A379234 Cf. A000203, A003714, A003987, A005820, A048724.
%Y A379234 Fixed points of A318467.
%Y A379234 Subsequence of A379236.
%K A379234 nonn,hard,more
%O A379234 1,1
%A A379234 _Antti Karttunen_, Jan 04 2025