A217259 - OEIS

%I #29 May 21 2018 03:14:48

%S 4,6,12,18,30,42,60,72,102,108,138,150,180,192,198,228,240,270,282,

%T 312,348,420,432,435,462,522,570,600,618,642,660,810,822,828,858,882,

%U 1020,1032,1050,1062,1092,1152,1230,1278,1290,1302,1320,1428,1452,1482,1488

%N Numbers n such that sigma(n+1) - sigma(n-1) = 2; sigma(n) = A000203(n) = sum of divisors of n.

%C Also numbers n such that antisigma(n+1) - antisigma(n-1) = 2*n - 1.

%C Antisigma(n) = A024816(n) = sum of nondivisors of n.

%C Union of A014574 (average of twin prime pairs) and sequence 435, 8576, 8826, … (= all terms < 100000).

%C If n = average of twin prime pairs (q < p) then antisigma(p) - antisigma(q) = 2*n - 1 = p + q - 1.

%C No term found below 2*10^9 to continue sequence 435, 8576, 8826, ... - _Michel Marcus_, Mar 19 2013

%H Jaroslav Krizek, <a href="/A217259/b217259.txt">Table of n, a(n) for n = 1..1227</a> (all terms < 100000)

%e Number 435 is in sequence because antisigma(436) - antisigma(434) = 94496 - 93627 = 869 = 2*435 - 1.

%t Flatten[Position[Partition[DivisorSigma[1,Range[1500]],3,1],_?(#[[3]]- #[[1]] == 2&),1,Heads->False]]+1 (* _Harvey P. Dale_, May 03 2018 *)

%o (PARI) isok(n) = (sigma(n+1) - sigma(n-1)) == 2; \\ _Michel Marcus_, May 20 2018

%Y Cf. A014574, A015886, A024816, A050507, A206768.

%Y Equals A054799 + 1. - _Michel Marcus_, May 21 2018

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 17 2013