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A307716
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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)).
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2
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1, 5, 10, 1, 14, 41, 58, 11, 50, 129, 160, 197, 119, 281, 328, 127, 110, 501, 568, 213, 89, 791, 874, 963, 53, 27, 1264, 457, 370, 1593, 1720, 1851, 71, 2127, 2276, 809, 1292, 2747, 2914, 3087, 1633, 1149, 34, 3831, 1007, 4227, 4438, 4661
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OFFSET
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1,2
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COMMENTS
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It appears that lim_{n->infinity} (1/n)*(A014285(n)/A007504(n)) = k, where k is a constant around 2/3.
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LINKS
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FORMULA
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a(n) = denominator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).
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MAPLE
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S1:= 0:S2:= 0:
for n from 1 to 100 do
p:= ithprime(n);
S1:= S1 + p;
S2:= S2 + n*p;
A[n]:= denom(S2/S1)
od:
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MATHEMATICA
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a[n_]:=Sum[i*Prime[i], {i, 1, n}]/Sum[Prime[i], {i, 1, n}];
Table[a[n]//Denominator, {n, 1, 48}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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