A345061 - OEIS

%I #11 Jul 06 2021 20:05:27

%S 1,1,2,3,4,2,6,5,7,2,10,2,12,2,4,11,16,1,18,12,4,2,22,2,21,2,20,18,28,

%T 2,30,21,4,2,8,1,36,2,4,4,40,4,42,30,4,2,46,2,43,1,4,36,52,20,8,2,4,2,

%U 58,8,60,2,2,43,8,4,66,48,4,6,70,7,72,2,2,54,12,8,78,4,61,2,82,18,8,2,4,10,88,4,12,66

%N a(n) = gcd(A071324(n), A206369(n)).

%H Antti Karttunen, <a href="/A345061/b345061.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = gcd(A071324(n), A206369(n)).

%F a(n) = gcd(A071324(n), A345060(n)) = gcd(A206369(n), A345060(n)).

%F a(n) = A071324(n) / A345062(n) = A206369(n) / A345063(n).

%t {1}~Join~Array[GCD[Total[-#*(-1)^Range[Length[#], 1, -1]] &@ Divisors[#], Times @@ (Sum[(-1)^(#2 - k)*#1^k, {k, 0, #2}] & @@@ FactorInteger[#])] &, 91, 2] (* _Michael De Vlieger_, Jul 06 2021, after _Amiram Eldar_ at A071324 and A206369 *)

%o (PARI)

%o A071324(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (-1)^(k+1)*d[k]); \\ From A071324

%o A206369(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ From A206369

%o A345061(n) = gcd(A071324(n), A206369(n));

%Y Cf. A071324, A206369, A345060, A345062, A345063.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 07 2021