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A007503 Number of subgroups of dihedral group: sigma(n) + d(n).
(Formerly M1321)
23
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.

Index entries for sequences related to groups

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,changed

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)