A325633 - OEIS

%I #8 May 21 2019 22:03:32

%S 1,1,1,1,1,6,1,1,1,2,1,4,1,2,3,1,1,3,1,2,1,2,1,12,1,2,1,28,1,6,1,1,3,

%T 2,1,1,1,2,1,10,1,2,1,4,1,2,1,4,1,1,3,2,1,2,1,8,1,2,1,4,1,2,1,1,1,6,1,

%U 2,1,2,1,3,1,2,1,4,1,2,1,2,1,2,1,28,1,2,1,4,1,2,1,4,1,2,5,12,1,1,1,1,1,2,1,2,3

%N a(n) = gcd(A009194(n), A325634(n)) = gcd(A009194(n), A091255(n, sigma(n))).

%H Antti Karttunen, <a href="/A325633/b325633.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>

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

%F a(n) = gcd(A009194(n), A325634(n)) = gcd(A009194(n), A091255(n, A000203(n))).

%o (PARI)

%o A009194(n) = gcd(n,sigma(n));

%o A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);

%o A325634(n) = A091255sq(n, sigma(n));

%o A325633(n) = gcd(A009194(n),A325634(n));

%Y Cf. A000203, A091255, A325634.

%Y Differs from A009194 for the first time at n=42, where a(42) = 2, while A009194(42) = 6.

%Y Differs from A325632 and A325640 for the first time at n=45, where a(45) = 1, while A325632(45) = 5 and A325640(45) = 3.

%K nonn

%O 1,6

%A _Antti Karttunen_, May 21 2019