A272206 Rounded barycenter of first n primes defined as a(n) = round(sum_{i=1..n}(i*prime(i)) / sum_{i=1..n}prime(i)).

1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45

Offset: 1

Author

Andres Cicuttin, May 21 2016

Keywords

• nonn

Crossrefs

Cf. A007504, A014285.

Programs

Mathematica

a[n_] := Sum[i*Prime[i], {i, 1, n}]/Sum[Prime[i], {i, 1, n}];
Table[a[n] // Round, {n, 1, 64}];

PARI

a(n) = round(sum(k=1, n, k*prime(k))/ sum(k=1, n, prime(k))); \\ Michel Marcus, May 22 2016

Formula

a(n) = round(sum_{i=1..n}(i*prime(i)) / sum_{i=1..n}prime(i)).

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