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A007503 Number of subgroups of dihedral group: sigma(n) + d(n).
(Formerly M1321)
24

%I M1321

%S 2,5,6,10,8,16,10,19,16,22,14,34,16,28,28,36,20,45,22,48,36,40,26,68,

%T 34,46,44,62,32,80,34,69,52,58,52,100,40,64,60,98,44,104,46,90,84,76,

%U 50,134,60,99,76,104,56,128,76,128,84,94,62,180,64,100,110,134

%N Number of subgroups of dihedral group: sigma(n) + d(n).

%C Essentially first differences of A257644. - _Franklin T. Adams-Watters_, Nov 05 2015

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A007503/b007503.txt">Table of n, a(n) for n = 1..1000</a>

%H David W. Jensen and Eric R. Bussian, <a href="http://www.jstor.org/stable/2686678">A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups</a>, Two-Year College Math. Jnl., 23 (1992), 150-152.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F G.f.: sum(k>=1, 1/(1-x^k)^2). - _Benoit Cloitre_, Apr 21 2003

%F G.f.: sum(i>=1, (1+i)*x^i/(1-x^i)). - _Jon Perry_, Jul 03 2004

%F a(n) = Sum(d|n, tau(p^d)), where tau is A000005 and p any prime. - _Enrique Pérez Herrero_, Apr 14 2012

%F a(n) = sum( d divides n, d+1 ). - _Joerg Arndt_, Apr 14 2013

%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(1+1/k)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 23 2018

%F a(n) = A000005(n) + A000203(n). - _Omar E. Pol_, Aug 19 2019

%p with(numtheory): seq(sigma(n)+tau(n), n=1..56) ; # _Zerinvary Lajos_, Jun 04 2008

%t A007503[n_]:=DivisorSum[n,DivisorSigma[0,2^#]&]; Array[A007503,20] (* _Enrique Pérez Herrero_, Apr 14 2012 *)

%o (PARI) a(n) = sumdiv(n,d, d+1 ); \\ _Joerg Arndt_, Apr 14 2013

%o (Haskell)

%o a007503 = sum . map (+ 1) . a027750_row'

%o -- _Reinhard Zumkeller_, Nov 09 2015

%Y Cf. A000005, A000203, A257644.

%Y Cf. A027750, A257644 (cummulative sums, start=1).

%K nonn

%O 1,1

%A _N. J. A. Sloane_, _Robert G. Wilson v_

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)