A206768 -id:A206768 - cp's OEIS frontend

A084293 a(n) = 2n + A054905(n).

436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161

Offset: 1

Labos Elemer, May 26 2003

The sequence begins 436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161, ?, 91, 87, 92, 122, 111, 1585396, 145, 94, 76627, 10283, 159, 772, 133, 122, 412, 194, 142, 964, 205, 374, 925, 6725, 209, ?, 1015, 178, ?, ?, 206, 146, ?, ..., where the other missing terms (designated by "?") are unknown, if they exist (see also A206768).

			To terms of A054905, where sigma(x+2n)=sigma(x)+2n replacing x+2n=y,x=y-2n, we get sigma(y)-2n=sigma(y-2n);
For several analogous sequences, the corresponding "mirror-solutions" can be easily constructed. See: e.g. A015913-A015918; A050507, A054799, A054903-A054906; A054982-A054987; A059118; A055009, A055458, A063500, etc.

Cf. A054905.

Composite x satisfying sigma(x-2n) = sigma(x) - 2n.

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

Original entry on oeis.org

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

Jaroslav Krizek, Mar 17 2013

nonn

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

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

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

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

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

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

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

cp's OEIS Frontend

A084293 a(n) = 2n + A054905(n).

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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.

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