A066886 Sum of the elements in any transversal of a prime(n) X prime(n) array containing the numbers from 1 to prime(n)^2 in standard order.

5, 15, 65, 175, 671, 1105, 2465, 3439, 6095, 12209, 14911, 25345, 34481, 39775, 51935, 74465, 102719, 113521, 150415, 178991, 194545, 246559, 285935, 352529, 456385, 515201, 546415, 612575, 647569, 721505, 1024255, 1124111, 1285745

Offset: 1

Author

Enoch Haga, Jan 22 2002

Keywords

• easy
• nonn

Comments

a(n) is the sum of the primes in a prime(n) X prime(n) example of Haga's conjecture (see link below).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Carlos Rivera, The prime puzzles & problems connection, conjecture 26, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A005097, A006003, A006254, A066883, A066885.

Programs

Maple

map(t -> t*(t^2+1)/2, [seq(ithprime(i),i=1..100)]); # Robert Israel, Apr 04 2018

Mathematica

a[n_] := Prime[n] (Prime[n]^2 + 1)/2; Table[a[n], {n, 50}]

PARI

apply(x->(x*(x^2+1)/2), primes(100)) \\ Michel Marcus, Apr 04 2018

Formula

a(n) = prime(n)*(prime(n)^2+1)/2, where prime(n) is the n-th prime.

a(n) = A006003(prime(n)). - Michel Marcus, Apr 04 2018

a(n) = A006254(n-1)^4 - A005097(n-1)^4, for n>1. - Dimitris Valianatos, Apr 10 2018

Extensions

Edited by Dean Hickerson, Jun 08 2002