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 A351559 #15 Feb 20 2022 11:00:41
%S A351559 0,2,1,0,1,2,1,0,0,2,3,8,9,2,3,0,1,2,1,0,1,2,3,0,0,10,1,8,5,2,1,0,1,2,
%T A351559 3,32,1,6,1,0,9,2,1,8,33,2,3,0,0,2,3,0,1,6,3,0,1,2,3,8,1,2,33,0,1,2,
%U A351559 65,0,1,2,3,0,1,2,1,12,1,10,5,0,16,2,3,0,1,18,7,0,1,2,9,8,1,2,7,0,1,2,35,0,65,2,33
%N A351559 a(n) = A048675(gcd(sigma(n), A019565(n))).
%H A351559 Antti Karttunen, <a href="/A351559/b351559.txt">Table of n, a(n) for n = 1..65537</a>
%H A351559 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A351559 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A351559 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A351559 a(n) = A048675(A351557(n)) = A048675(gcd(sigma(n), A019565(n))).
%F A351559 a(n) = n AND A351560(n), where AND is bitwise-and, A004198.
%t A351559 Table[If[# == 1, 0, Total[#2*2^PrimePi[#1] & @@@ FactorInteger[#]]/2] &@ GCD[DivisorSigma[1, n], Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 103}] (* _Michael De Vlieger_, Feb 20 2022 *)
%o A351559 (PARI)
%o A351559 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351559 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A351559 A351559(n) = A048675(gcd(sigma(n), A019565(n)));
%Y A351559 Cf. A000203, A004198, A007947, A019565, A080398, A351557, A351560.
%Y A351559 Cf. also A324644, A351558.
%K A351559 nonn,look
%O A351559 1,2
%A A351559 _Antti Karttunen_, Feb 19 2022