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 A007503 Number of subgroups of dihedral group: sigma(n) + d(n). (Formerly M1321) 24
 2, 5, 6, 10, 8, 16, 10, 19, 16, 22, 14, 34, 16, 28, 28, 36, 20, 45, 22, 48, 36, 40, 26, 68, 34, 46, 44, 62, 32, 80, 34, 69, 52, 58, 52, 100, 40, 64, 60, 98, 44, 104, 46, 90, 84, 76, 50, 134, 60, 99, 76, 104, 56, 128, 76, 128, 84, 94, 62, 180, 64, 100, 110, 134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Essentially first differences of A257644. - Franklin T. Adams-Watters, Nov 05 2015 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 David W. Jensen and Eric R. Bussian, A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups, Two-Year College Math. Jnl., 23 (1992), 150-152. FORMULA G.f.: sum(k>=1, 1/(1-x^k)^2). - Benoit Cloitre, Apr 21 2003 G.f.: sum(i>=1, (1+i)*x^i/(1-x^i)). - Jon Perry, Jul 03 2004 a(n) = Sum(d|n, tau(p^d)), where tau is A000005 and p any prime. - Enrique Pérez Herrero, Apr 14 2012 a(n) = sum( d divides n, d+1 ). - Joerg Arndt, Apr 14 2013 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 a(n) = A000005(n) + A000203(n). - Omar E. Pol, Aug 19 2019 MAPLE with(numtheory): seq(sigma(n)+tau(n), n=1..56) ; # Zerinvary Lajos, Jun 04 2008 MATHEMATICA A007503[n_]:=DivisorSum[n, DivisorSigma[0, 2^#]&]; Array[A007503, 20] (* Enrique Pérez Herrero, Apr 14 2012 *) PROG (PARI) a(n) = sumdiv(n, d, d+1 ); \\ Joerg Arndt, Apr 14 2013 (Haskell) a007503 = sum . map (+ 1) . a027750_row' -- Reinhard Zumkeller, Nov 09 2015 CROSSREFS Cf. A000005, A000203, A257644. Cf. A027750, A257644 (cummulative sums, start=1). Sequence in context: A226810 A054463 A295741 * A184418 A112967 A244731 Adjacent sequences:  A007500 A007501 A007502 * A007504 A007505 A007506 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)