A294612 Denominator of the contraharmonic mean of the first n primes.

1, 5, 5, 17, 7, 41, 29, 77, 25, 43, 80, 197, 119, 281, 164, 127, 110, 501, 284, 639, 89, 791, 437, 963, 265, 1161, 632, 457, 185, 1593, 860, 1851, 497, 709, 1138, 2427, 323, 2747, 1457, 1029, 1633, 3447, 1819, 3831, 53, 1409, 2219, 4661, 1222, 5117, 2675, 1863

Offset

1,2

Comments

Is there any n > 1 for which a(n) = 1?

There are only two terms < 101 for n = 40..10^7: a(45)=53 and a(253)=13. - Zak Seidov, Dec 09 2017

Links

Table of n, a(n) for n=1..52.

Formula

a(n) = denominator( Sum_{k=1..n} prime(k)^2/Sum_{k=1..n} prime(k) ).

a(n) = denominator( A024450(n)/A007504(n) ).

Mathematica

Array[ Denominator@ ContraharmonicMean@ Prime@ Range@# &, 52] (* slightly modified by Robert G. Wilson v, Dec 10 2017 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, prime(k)^2)/sum(k=1, n, prime(k))); \\ Michel Marcus, Dec 01 2017

Crossrefs

Cf. A007504 (sum of the first n primes), A024450 (sum of squares of the first n primes), A296199 (numerators).

Sequence in context: A273544 A273703 A253065 * A246332 A300784 A273326

Adjacent sequences: A294609 A294610 A294611 * A294613 A294614 A294615

Keyword

nonn,frac

Author

Andres Cicuttin, Nov 04 2017

Status

approved