A275470 Half the difference between the larger and smaller terms of the n-th amicable pair (x,y) given in A259933.

32, 13, 152, 272, 68, 56, 1155, 560, 32, 2025, 6532, 9009, 4490, 11835, 392, 8775, 5756, 13210, 2240, 2288, 9032, 2860, 42272, 40652, 55426, 21592, 8944, 8575, 5840, 1755, 34648, 38072, 4664, 33536, 38296, 57796, 35296, 30555, 10856, 41384

Offset

1,1

Comments

Each term represents the radius of an interval (x,y), where x (A260086) and y (A260087) form a pair of amicable numbers (A259933). The midpoint and length of each interval can be found in A275316 and A275469, respectively.

A term will be odd if and only if y-x = 2 mod 4. This occurs when x and y have the same parity but their average has the opposite parity.

This sequence is a rearrangement of A162884 (which is based on A002025, A002046, and A066539). The first ten indices for which a(n) does not equal A162884(n) are n = 9, 10, 11, 15, 16, 33, 34, 35, 41, 42.

Links

Timothy L. Tiffin, Table of n, a(n) for n = 1..142

VaxaSoftware, List of amicable numbers from 1 to 20,000,000 [142 pairs].

Formula

a(n) = [A260087(n) - A260086(n)]/2 = A275469(n)/2.

Example

a(1) = (284-220)/2 = 64/2 = 32, a(2) = (1210-1184)/2 = 26/2 = 13, and a(3) = (2924-2620)/2 = 304/2 = 152.

Crossrefs

Cf. A002025, A002046, A066539, A260086, A260087, A162884, A259933, A275316, A275469.

Sequence in context: A305038 A305584 A316691 * A162884 A029771 A302684

Adjacent sequences: A275467 A275468 A275469 * A275471 A275472 A275473

Keyword

nonn

Author

Timothy L. Tiffin, Jul 28 2016

Status

approved