A217259 Numbers n such that sigma(n+1) - sigma(n-1) = 2; sigma(n) = A000203(n) = sum of divisors of n.

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, 180, 192, 198, 228, 240, 270, 282, 312, 348, 420, 432, 435, 462, 522, 570, 600, 618, 642, 660, 810, 822, 828, 858, 882, 1020, 1032, 1050, 1062, 1092, 1152, 1230, 1278, 1290, 1302, 1320, 1428, 1452, 1482, 1488

Offset: 1

Author

Jaroslav Krizek, Mar 17 2013

Keywords

• nonn

Comments

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

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

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

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

No term found below 2*10^9 to continue sequence 435, 8576, 8826, ... - Michel Marcus, Mar 19 2013

Examples

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

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1227 (all terms < 100000)

Crossrefs

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

Equals A054799 + 1. - Michel Marcus, May 21 2018

Programs

Mathematica

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

PARI

isok(n) = (sigma(n+1) - sigma(n-1)) == 2; \\ Michel Marcus, May 20 2018