|
%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
|
