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%I #21 Mar 08 2024 08:28:07
%S 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,
%T 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,
%U 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
%N First difference sequence of A002191. Differences between possible values for sum of divisors of n.
%H Michael De Vlieger, <a href="/A083531/b083531.txt">Table of n, a(n) for n = 1..10000</a>
%e 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).
%e From _Michael De Vlieger_, Jul 22 2017: (Start)
%e First position of values:
%e Value First position
%e 1 2
%e 2 1
%e 3 10
%e 4 6
%e 5 30
%e 6 24
%e 7 277
%e 8 165
%e 9 509
%e 10 150
%e 11 824
%e 12 400
%e 13 10970
%e 14 1400
%e 15 10448
%e 16 1182
%e 17 18731
%e 18 2218
%e 19 209237
%e 20 3420
%e 21 127385
%e 22 6910
%e 23 28899
%e 24 5377
%e (End)
%t t=Table[DivisorSigma[1, w], {w, 1, 25000}]; u=Union[%]; Delete[u-RotateRight[u], 1]
%t (* Second program: *)
%t With[{nn = 300}, Differences@ TakeWhile[Union@ DivisorSigma[1, Range@ nn], # < nn &]] (* _Michael De Vlieger_, Jul 22 2017 *)
%Y Cf. A002191, A007609, A007369, A083532, A083533, A083534, A083535, A083536, A109323 (start of record gaps in A002191).
%K nonn
%O 1,1
%A _Labos Elemer_, May 20 2003
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