login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259933 Amicable pairs (x < y) ordered by nondecreasing sum (x + y) and then by increasing x. 14
220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 66928, 66992, 67095, 71145, 63020, 76084, 69615, 87633, 79750, 88730, 100485, 124155, 122368, 123152, 122265, 139815, 141664, 153176, 142310, 168730, 171856, 176336, 176272, 180848, 185368, 203432, 196724, 202444, 280540, 365084, 308620, 389924 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A pair of numbers x and y is called amicable if the sum of the proper divisors (or aliquot parts) of either one is equal to the other.

By definition a property of the amicable pair (x, y) is that x + y = sigma(x) = sigma(y).

The amicable pairs (x < y) are adjacent to each other in the list.

Also A260086 and A260087 interleaved.

Another version (A259180) lists the amicable pairs (x < y) ordered by increasing x.

Amicable numbers A063990 are the terms of this sequence in increasing order.

First differs from both A063990 and A259180 at a(17).

LINKS

Table of n, a(n) for n=1..48.

Laszlo Hars, Performance compared to mathematica Julia-users (2014)

Khelleos, Amicable numbers, CyberForum.ru (2011)

OEIS Wiki, Amicable numbers (This page needs work)

Wikipédia, Barátságos számok (contains a mistake: A063990 should be replaced with A259933)

FORMULA

a(2n-1) + a(2n) = A000203(a(2n-1)) = A000203(a(2n)) = A259953(n).

EXAMPLE

-----------------------------------

       Amicable pair         Sum

          x      y          x + y

-----------------------------------

n     A260086 A260087      A259953

-----------------------------------

1        220     284          504

2       1184    1210         2394

3       2620    2924         5544

4       5020    5564        10584

5       6232    6368        12600

6      10744   10856        21600

7      12285   14595        26880

8      17296   18416        35712

9      66928   66992       133920

10     67095   71145       138240

11     63020   76084       139104

12     69615   87633       157248

...      ...     ...          ...

32    609928  686072      1296000

33    643336  652664      1296000

...

The sum of the proper divisors (or aliquot parts) of 220 is 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284. On the other hand the sum of the proper divisors (or aliquot parts) of 284 is 1 + 2 + 4 + 71 + 142 = 220. Note that 220 + 284 = sigma(220) = sigma(284) = 504. The sum 220 + 284 = 504 is the smallest sum of an amicable pair, so a(1) = 220 and a(2) = 284.

Note that some pairs (x, y) share the same sum (x + y), for example: (609928 + 686072) = (643336 + 652664) = sigma(609928) = sigma(686072) = sigma(643336) = sigma(652664) = 1296000, thus in the list first appears the pair (609928, 686072) and then (643336, 652664) because 609928 < 643336.

CROSSREFS

Cf. A000203, A063990, A259180, A259953, A260086, A260087.

Sequence in context: A255215 A063990 A259180 * A273259 A262624 A262622

Adjacent sequences:  A259930 A259931 A259932 * A259934 A259935 A259936

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jul 09 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 21:15 EST 2017. Contains 295919 sequences.