A088580 a(n) = 1 + sigma(n).

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, 43, 41, 57, 31, 73, 33, 64, 49, 55, 49, 92, 39, 61, 57, 91, 43, 97, 45, 85, 79, 73, 49, 125, 58, 94, 73, 99, 55, 121, 73, 121, 81, 91, 61, 169, 63, 97, 105, 128, 85, 145, 69, 127, 97

Offset: 1

Author

James East, Nov 20 2003

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Crossrefs

Cf. A000203 (sum of divisors of n).

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

Programs

Haskell

a088580 = (+ 1) . a000203  -- Reinhard Zumkeller, Dec 20 2014

Magma

[1+SumOfDivisors(n): n in [1..100]]; // Vincenzo Librandi, May 30 2015

Maple

map(1+numtheory:-sigma, [$1..1000]); # Robert Israel, May 29 2015

Mathematica

Table[1 + DivisorSigma[1, n], {n, 100}] (* Robert Price, May 29 2015 *)

Formula

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

G.f.: x/(1 - x) + Sum_{k>=1} x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 17 2017