cp's OEIS Frontend

A307716 Denominator of the barycenter of first n primes defined as a(n) = denominator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).

%I A307716 #39 Jul 08 2019 12:31:09
%S A307716 1,5,10,1,14,41,58,11,50,129,160,197,119,281,328,127,110,501,568,213,
%T A307716 89,791,874,963,53,27,1264,457,370,1593,1720,1851,71,2127,2276,809,
%U A307716 1292,2747,2914,3087,1633,1149,34,3831,1007,4227,4438,4661
%N A307716 Denominator of the barycenter of first n primes defined as a(n) = denominator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).
%C A307716 It appears that lim_{n->infinity} (1/n)*(A014285(n)/A007504(n)) = k, where k is a constant around 2/3.
%C A307716 a(n) = A007504(n) if and only if n is in A307414. - _Robert Israel_, Jul 08 2019
%H A307716 Robert Israel, <a href="/A307716/b307716.txt">Table of n, a(n) for n = 1..10000</a>
%F A307716 a(n) = denominator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).
%F A307716 a(n) = denominator(A014285(n)/A007504(n)).
%p A307716 S1:= 0:S2:= 0:
%p A307716 for n from 1 to 100 do
%p A307716   p:= ithprime(n);
%p A307716   S1:= S1 + p;
%p A307716   S2:= S2 + n*p;
%p A307716   A[n]:= denom(S2/S1)
%p A307716 od:
%p A307716 seq(A[i],i=1..100); # _Robert Israel_, Jul 08 2019
%t A307716 a[n_]:=Sum[i*Prime[i], {i, 1, n}]/Sum[Prime[i], {i, 1, n}];
%t A307716 Table[a[n]//Denominator, {n, 1, 48}]
%o A307716 (PARI) a(n) = my(vp=primes(n)); denominator(sum(i=1, n, i*vp[i])/sum(i=1, n, vp[i])) \\ _Michel Marcus_, Apr 25 2019
%Y A307716 Cf. A306834 (numerators), A272206, A007504, A014285, A307414.
%K A307716 nonn,frac,look
%O A307716 1,2
%A A307716 _Andres Cicuttin_, Apr 25 2019