A086148 Sum of the orders of the elements in the dihedral group D_2n.

3, 7, 13, 19, 31, 33, 57, 59, 79, 83, 133, 101, 183, 157, 177, 203, 307, 219, 381, 271, 343, 377, 553, 349, 571, 523, 601, 529, 871, 501, 993, 747, 843, 887, 973, 743, 1407, 1105, 1177, 983, 1723, 987, 1893, 1309, 1371, 1613, 2257, 1293, 2199, 1663, 2013

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 25 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057660.

Programs

Mathematica

f[p_, e_] := (p^(2*e+1)+1)/(p+1); a[1] = 3; a[n_] := 2*n + Times @@ (f @@@ FactorInteger[n]); Array[a, 50] (* Amiram Eldar, Jul 31 2019 *)

PARI

a(n) = 2*n + sumdivmult(n, d, d*eulerphi(d)); \\ Michel Marcus, Feb 16 2024

Python

from sympy import factorint, prod
a = lambda n: 2*n + prod((p**(2*e+1)+1)//(p+1) for p,e in factorint(n).items()) # Darío Clavijo, Feb 15 2024

Formula

a(n) = 2*n + Sum_{d|n} d*phi(d). - Vladeta Jovovic, Aug 27 2003

Extensions

More terms from Vladeta Jovovic, Aug 27 2003