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A062249 a(n) = n + d(n), where d(n) = number of divisors of n, cf. A000005. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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)

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 *)

PROG

(PARI) { for (n=1, 1000, write("b062249.txt", n, " ", n + numdiv(n)) ) } \\ Harry J. Smith, Aug 03 2009

(Haskell)

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

(Python)

from sympy.ntheory import divisor_count

print [n + divisor_count(n) for n in xrange(101)] # Indranil Ghosh, Apr 12 2017

CROSSREFS

Cf. A007503, A060710, A000005, A049820.

Cf. A064491 (iteration, start=1).

Sequence in context: A085888 A187325 A112233 * A081404 A081516 A255873

Adjacent sequences:  A062246 A062247 A062248 * A062250 A062251 A062252

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Formula and more terms from Vladeta Jovovic, Jul 03 2001

STATUS

approved

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Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)