A062249 a(n) = n + d(n), where d(n) = number of divisors of n, cf. A000005.

2, 4, 5, 7, 7, 10, 9, 12, 12, 14, 13, 18, 15, 18, 19, 21, 19, 24, 21, 26, 25, 26, 25, 32, 28, 30, 31, 34, 31, 38, 33, 38, 37, 38, 39, 45, 39, 42, 43, 48, 43, 50, 45, 50, 51, 50, 49, 58, 52, 56, 55, 58, 55, 62, 59, 64, 61, 62, 61, 72, 63, 66, 69, 71, 69, 74, 69, 74, 73, 78, 73

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 01 2001

Keywords

• nonn

Comments

Number of cyclic subgroups of dihedral group with 2n elements.

a(n) is the n-th smallest number not a divisor of n. - J. Lowell, Apr 06 2008

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A007503, A060710, A000005, A049820.

Cf. A064491 (iteration, start=1).

Programs

Haskell

a062249 n = a000005 n + n  -- Reinhard Zumkeller, Mar 29 2014

Maple

with(numtheory):seq(n+tau(n), n=1..71) ; # Zerinvary Lajos, Jun 04 2008

Mathematica

Table[n + DivisorSigma[0, n], {n, 100}] (* Indranil Ghosh, Apr 12 2017 *)

PARI

a(n) = n + numdiv(n) \\ Harry J. Smith, Aug 03 2009

Python

from sympy.ntheory import divisor_count
[n + divisor_count(n) for n in range(101)] # Indranil Ghosh, Apr 12 2017

Formula

a(n) = n + A000005(n). - Omar E. Pol, Dec 12 2008

From Ilya Gutkovskiy, Apr 12 2017: (Start)

G.f.: x/(1 - x)^2 + Sum_{k>=1} x^k/(1 - x^k).

Dirichlet g.f.: zeta(s)^2 + zeta(s-1). (End)

Extensions

Formula and more terms from Vladeta Jovovic, Jul 03 2001