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A309036 a(n) = gcd(A007504(n), A014285(n)).

%I A309036 #21 Sep 08 2022 08:46:21
%S A309036 2,1,1,17,2,1,1,7,2,1,1,1,2,1,1,3,4,1,1,3,8,1,1,1,20,43,1,3,4,1,1,1,
%T A309036 28,1,1,3,2,1,1,1,2,3,107,1,4,1,1,1,2,7,1,1,10,3,1,1,30,1,1,1,2,5,1,1,
%U A309036 2,1,1,3,2,1,1,1,2,1,1,1,142,1,1,3,4,1,1,11,2,1,1,1,10
%N A309036 a(n) = gcd(A007504(n), A014285(n)).
%C A309036 a(n) is even if n == 1 (mod 4).
%H A309036 Robert Israel, <a href="/A309036/b309036.txt">Table of n, a(n) for n = 1..10000</a>
%F A309036 a(n) = A007504(n)/A307716(n) = A014285(n)/A306834(n).
%e A309036 a(4) = gcd(2+3+5+7, 1*2+2*3+3*5+4*7) = gcd(17,51) = 17.
%p A309036 S1:= 0: S2:= 0:
%p A309036 for n from 1 to 100 do
%p A309036   p:= ithprime(n);
%p A309036   S1:= S1 + p;
%p A309036   S2:= S2 + n*p;
%p A309036   A[n]:= igcd(S1,S2);
%p A309036 od:
%p A309036 seq(A[i],i=1..100);
%t A309036 GCD @@ # & /@ Rest@ Nest[Append[#1, {#1[[-1, 1]] + #3, #1[[-1, -1]] + #2 #3}] & @@ {#1, #2, Prime@ #2} & @@ {#, Length@ #} &, {{0, 0}}, 89] (* _Michael De Vlieger_, Jul 08 2019 *)
%o A309036 (PARI) a(n) = gcd(sum(k=1, n, prime(k)), sum(k=1, n, k*prime(k))); \\ _Michel Marcus_, Jul 09 2019
%o A309036 (Magma) p:=PrimesUpTo(1000);[Gcd(&+[p[j]:j in [1..m]],&+[j*p[j]:j in [1..m]]): m in [1..90]]; // _Marius A. Burtea_, Jul 09 2019
%Y A309036 Cf. A007504, A014285, A306834, A307414 (a(n)=1), A307716, A309055, A309056.
%K A309036 nonn
%O A309036 1,1
%A A309036 _Robert Israel_, Jul 08 2019