%I #15 Feb 20 2022 11:00:41

%S 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 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 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 a(n) = A048675(gcd(sigma(n), A019565(n))).

%H Antti Karttunen, <a href="/A351559/b351559.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A048675(A351557(n)) = A048675(gcd(sigma(n), A019565(n))).

%F a(n) = n AND A351560(n), where AND is bitwise-and, A004198.

%t 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 (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

%o A351559(n) = A048675(gcd(sigma(n), A019565(n)));

%Y Cf. A000203, A004198, A007947, A019565, A080398, A351557, A351560.

%Y Cf. also A324644, A351558.

%K nonn,look

%O 1,2

%A _Antti Karttunen_, Feb 19 2022