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A351558 a(n) = A048675(gcd(n, A019565(n))).

%I A351558 #16 Feb 20 2022 11:00:31
%S A351558 0,0,0,2,0,4,2,0,0,0,0,0,0,0,8,6,0,0,2,0,4,0,16,0,0,0,0,2,8,0,6,0,0,0,
%T A351558 0,0,0,0,0,34,0,0,10,0,0,4,0,0,0,0,0,2,32,0,2,20,8,0,0,0,4,0,0,10,0,0,
%U A351558 2,0,64,0,4,0,0,0,0,2,0,8,2,0,0,0,0,0,0,68,0,2,16,0,2,8,0,0,0,4,0,0,0,2,4,0,66
%N A351558 a(n) = A048675(gcd(n, A019565(n))).
%H A351558 Antti Karttunen, <a href="/A351558/b351558.txt">Table of n, a(n) for n = 0..65537</a>
%H A351558 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A351558 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A351558 a(n) = A048675(A351556(n)) = A048675(gcd(n, A019565(n))).
%F A351558 a(n) = n AND A087207(n), where AND is bitwise-and, A004198.
%t A351558 Table[If[# == 1, 0, Total[#2*2^PrimePi[#1] & @@@ FactorInteger[#]]/2] &@ GCD[n, Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 102}] (* _Michael De Vlieger_, Feb 20 2022 *)
%o A351558 (PARI)
%o A351558 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351558 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A351558 A351558(n) = A048675(gcd(n, A019565(n)));
%Y A351558 Cf. A004198, A007947, A019565, A087207, A351556.
%Y A351558 Cf. also A324198, A351559.
%K A351558 nonn,look
%O A351558 0,4
%A A351558 _Antti Karttunen_, Feb 19 2022