A083531 - OEIS

A083531

First difference sequence of A002191. Differences between possible values for sum of divisors of n.

2, 1, 2, 1, 1, 4, 1, 1, 1, 3, 2, 4, 4, 2, 1, 1, 4, 2, 1, 1, 2, 2, 4, 6, 2, 1, 3, 2, 1, 5, 4, 2, 4, 2, 4, 6, 1, 2, 3, 2, 4, 2, 4, 2, 2, 2, 6, 1, 3, 2, 1, 1, 4, 1, 5, 2, 4, 6, 2, 4, 2, 2, 2, 2, 4, 3, 3, 2, 4, 2, 1, 3, 6, 2, 1, 3, 2, 4, 6, 2, 4, 1, 5, 2, 4, 2, 4, 6, 2, 6, 4, 3, 1, 2, 2, 4, 2, 4, 2, 6, 2, 2, 2, 4, 6

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

OFFSET

1,1

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

8 and 12 are the 6th and 7th possible values for sigma(x), since they are sum of divisors of x = 7 and x = 11 respectively, while 9, 10, 11 are impossible ones so 12 - 8 = 4 = a(6) = A002191(7) - A002191(6).

From Michael De Vlieger, Jul 22 2017: (Start)

First position of values:

Value First position

1 2

2 1

3 10

4 6

5 30

6 24

7 277

8 165

9 509

10 150

11 824

12 400

13 10970

14 1400

15 10448

16 1182

17 18731

18 2218

19 209237

20 3420

21 127385

22 6910

23 28899

24 5377

(End)

MATHEMATICA

t=Table[DivisorSigma[1, w], {w, 1, 25000}]; u=Union[%]; Delete[u-RotateRight[u], 1]

(* Second program: *)

With[{nn = 300}, Differences@ TakeWhile[Union@ DivisorSigma[1, Range@ nn], # < nn &]] (* Michael De Vlieger, Jul 22 2017 *)

CROSSREFS

Cf. A002191, A007609, A007369, A083532, A083533, A083534, A083535, A083536, A109323 (start of record gaps in A002191).

Sequence in context: A134303 A078997 A024680 * A003417 A358549 A158986

Adjacent sequences: A083528 A083529 A083530 * A083532 A083533 A083534

KEYWORD

nonn

AUTHOR

Labos Elemer, May 20 2003

STATUS

approved