A258430 -id:A258430

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A088580

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

+10
24

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

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

EXAMPLE

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

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 *)

PROG

(Haskell)

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

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

CROSSREFS

Cf. A000203 (sum of divisors of n).

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

KEYWORD

easy,nonn

AUTHOR

James East, Nov 20 2003

STATUS

approved

A065512

Numbers n such that sigma(n) + 1 is prime.

+10
8

1, 3, 5, 6, 10, 11, 12, 17, 20, 22, 24, 26, 27, 29, 30, 38, 41, 42, 45, 46, 51, 55, 59, 62, 68, 69, 71, 77, 82, 85, 88, 91, 99, 101, 104, 105, 106, 107, 108, 114, 116, 118, 125, 126, 132, 135, 136, 137, 140, 141, 145, 146, 147, 149, 150, 155, 158, 160, 161

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n=1..1000

OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

EXAMPLE

sigma(10) + 1 = 18 + 1 = 19 (prime). sigma(24) + 1 = 60 + 1 = 61 (prime).

MAPLE

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

MATHEMATICA

Select[ Range[170], PrimeQ[ DivisorSigma[1, # ] + 1] & ]

PROG

(PARI) { n=0; for (m=1, 10^9, if (isprime(sigma(m) + 1), write("b065512.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 20 2009

(Magma) [n: n in [1..200] | IsPrime(1+SumOfDivisors(n))]; // Vincenzo Librandi, May 30 2015

CROSSREFS

Cf. A000203, A088580, A258430.

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Nov 26 2001

STATUS

approved

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