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A217259 Numbers n such that sigma(n+1) - sigma(n-1) = 2; sigma(n) = A000203(n) = sum of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

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

Sequence in context: A061715 A280469 A072570 * A014574 A258838 A034425

Adjacent sequences:  A217256 A217257 A217258 * A217260 A217261 A217262

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Mar 17 2013

STATUS

approved

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Last modified September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)