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a(n) = n + d(n), where d(n) = number of divisors of n, cf. A000005.
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%I #44 Jul 08 2023 15:47:22

%S 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,

%T 30,31,34,31,38,33,38,37,38,39,45,39,42,43,48,43,50,45,50,51,50,49,58,

%U 52,56,55,58,55,62,59,64,61,62,61,72,63,66,69,71,69,74,69,74,73,78,73

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

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

%C a(n) is the n-th smallest number not a divisor of n. - _J. Lowell_, Apr 06 2008

%H Harry J. Smith, <a href="/A062249/b062249.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = n + A000005(n). - _Omar E. Pol_, Dec 12 2008

%F From _Ilya Gutkovskiy_, Apr 12 2017: (Start)

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

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

%p with(numtheory):seq(n+tau(n), n=1..71) ; # _Zerinvary Lajos_, Jun 04 2008

%t Table[n + DivisorSigma[0, n], {n, 100}] (* _Indranil Ghosh_, Apr 12 2017 *)

%o (PARI) a(n) = n + numdiv(n) \\ _Harry J. Smith_, Aug 03 2009

%o (Haskell)

%o a062249 n = a000005 n + n -- _Reinhard Zumkeller_, Mar 29 2014

%o (Python)

%o from sympy.ntheory import divisor_count

%o [n + divisor_count(n) for n in range(101)] # _Indranil Ghosh_, Apr 12 2017

%Y Cf. A007503, A060710, A000005, A049820.

%Y Cf. A064491 (iteration, start=1).

%K nonn

%O 1,1

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

%E Formula and more terms from _Vladeta Jovovic_, Jul 03 2001