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

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, 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, 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

Offset: 1

Author

Robert Israel, Jul 08 2019

Keywords

• nonn

Comments

a(n) is even if n == 1 (mod 4).

Examples

			a(4) = gcd(2+3+5+7, 1*2+2*3+3*5+4*7) = gcd(17,51) = 17.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A014285, A306834, A307414 (a(n)=1), A307716, A309055, A309056.

Programs

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

Maple

S1:= 0: S2:= 0:
for n from 1 to 100 do
  p:= ithprime(n);
  S1:= S1 + p;
  S2:= S2 + n*p;
  A[n]:= igcd(S1,S2);
od:
seq(A[i],i=1..100);

Mathematica

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 *)

PARI

a(n) = gcd(sum(k=1, n, prime(k)), sum(k=1, n, k*prime(k))); \\ Michel Marcus, Jul 09 2019

Formula

a(n) = A007504(n)/A307716(n) = A014285(n)/A306834(n).