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a(n) = 1 + sigma(n).
24

%I #31 Sep 08 2022 08:45:12

%S 2,4,5,8,7,13,9,16,14,19,13,29,15,25,25,32,19,40,21,43,33,37,25,61,32,

%T 43,41,57,31,73,33,64,49,55,49,92,39,61,57,91,43,97,45,85,79,73,49,

%U 125,58,94,73,99,55,121,73,121,81,91,61,169,63,97,105,128,85,145,69,127,97

%N a(n) = 1 + sigma(n).

%C Number of reflection subgroups of the (dihedral) Coxeter group of type I_2(n).

%H Reinhard Zumkeller, <a href="/A088580/b088580.txt">Table of n, a(n) for n = 1..10000</a>

%H OEIS Wiki, <a href="https://oeis.org/wiki/Cyclotomic Polynomials at x=n, n! and sigma(n)">Cyclotomic Polynomials at x=n, n! and sigma(n)</a>

%F a(n) = 1 + A000203(n).

%F G.f.: x/(1 - x) + Sum_{k>=1} x^k/(1 - x^k)^2. - _Ilya Gutkovskiy_, Mar 17 2017

%e a(2)=4. If W=<s, t|s^2=t^2=1, st=ts> then the reflection subgroups are {1}, <s>, <t>, <s, t>.

%p map(1+numtheory:-sigma, [$1..1000]); # _Robert Israel_, May 29 2015

%t Table[1 + DivisorSigma[1, n], {n, 100}] (* _Robert Price_, May 29 2015 *)

%o (Haskell)

%o a088580 = (+ 1) . a000203 -- _Reinhard Zumkeller_, Dec 20 2014

%o (Magma) [1+SumOfDivisors(n): n in [1..100]]; // _Vincenzo Librandi_, May 30 2015

%Y Cf. A000203 (sum of divisors of n).

%Y Cf. A065512 (indices of primes in this sequence), A258430 (corresponding primes).

%K easy,nonn

%O 1,1

%A _James East_, Nov 20 2003