A229738 a(n) = p^2*(p^2+2*p-1)/2, where p = prime(n).

14, 63, 425, 1519, 8591, 16393, 46529, 71839, 151823, 377609, 491071, 987049, 1480961, 1787983, 2542559, 4092713, 6262319, 7148041, 10374079, 13061231, 14585473, 19964959, 24297503, 32072129, 45172609, 53055401, 57362863, 66759119, 71868169, 82960193, 132112639, 149489471, 178699649, 189326479, 249739049

Offset: 1

Author

N. J. A. Sloane, Oct 05 2013

Keywords

• nonn

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• L. Kaylor, D. Offner, Counting matrices over a finite field with all eigenvalues in the field, Involve, a Journal of Mathematics, Vol. 7 (2014), No. 5, 627-645. [DOI]
• Michael Knapp, Two by Two Matrices with Both Eigenvalues in Z/pZ, Math. Mag., Vol. 79, No. 2, April 2006.
• G. Olsavsky, The Number of 2 by 2 Matrices over Z/pZ with Eigenvalues in the Same Field, Math. Mag., 76 (2003), 314-317.

Crossrefs

Cf. A229739, A255499.

Programs

Magma

[p^2*(p^2+2*p-1)/2: p in PrimesUpTo(200)]; // Bruno Berselli, Oct 07 2013

Mathematica

Table[Prime[n]^2 (Prime[n]^2 + 2 Prime[n] - 1)/2, {n, 40}] (* Bruno Berselli, Oct 07 2013 *)
#^2 (#^2+2#-1)/2&/@Prime[Range[40]] (* Harvey P. Dale, Mar 13 2017 *)

PARI

a(n)=p=prime(n);p^2*(p^2+2*p-1)/2 \\ Anders Hellström, Sep 04 2015

PARI

lista(nn) = forprime(p=2, nn, print1(p^2*(p^2+2*p-1)/2, ", ")); \\ Michel Marcus, Sep 04 2015