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A306834 Numerator of the barycenter of first n primes defined as a(n) = numerator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)). 4
1, 8, 23, 3, 53, 184, 303, 65, 331, 952, 1293, 1737, 1135, 2872, 3577, 1475, 1357, 6526, 7799, 3073, 1344, 12490, 14399, 16535, 948, 502, 24367, 9121, 7631, 33914, 37851, 42043, 1663, 51290, 56505, 20647, 33875, 73944, 80457, 87377, 47358, 34106, 1033, 119023, 31972, 137042, 146959, 157663 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that lim_{n->infinity} (1/n)*(A014285(n)/A007504(n)) = k, where k is a constant around 2/3.

LINKS

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

FORMULA

a(n) = numerator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)).

a(n) = numerator(A014285(n)/A007504(n)).

MAPLE

N:= 100: # for a(1)..a(N)

Primes:= map(ithprime, [$1..N]):

S1:= ListTools:-PartialSums(Primes):

S2:= ListTools:-PartialSums(zip(`*`, Primes, [$1..N])):

map(numer, zip(`/`, S2, S1)); # Robert Israel, Apr 07 2019

MATHEMATICA

a[n_]:=Sum[i*Prime[i], {i, 1, n}]/Sum[Prime[i], {i, 1, n}];

Table[a[n]//Numerator, {n, 1, 40}]

PROG

(PARI) a(n) = numerator(sum(i=1, n, i*prime(i))/sum(i=1, n, prime(i))); \\ Michel Marcus, Mar 15 2019

CROSSREFS

Cf. A272206, A007504, A014285.

Sequence in context: A117613 A215740 A304177 * A109271 A029755 A022420

Adjacent sequences:  A306831 A306832 A306833 * A306835 A306836 A306837

KEYWORD

nonn,frac,look

AUTHOR

Andres Cicuttin, Mar 12 2019

STATUS

approved

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Last modified February 26 20:23 EST 2020. Contains 332295 sequences. (Running on oeis4.)