A275470 -id:A275470 - cp's OEIS frontend

A275316 Average of amicable pairs (x,y), ordered by the sum x+y given in A259953.

252, 1197, 2772, 5292, 6300, 10800, 13440, 17856, 66960, 69120, 69552, 78624, 84240, 112320, 122760, 131040, 147420, 155520, 174096, 178560, 194400, 199584, 322812, 349272, 374976, 378000, 446400, 477603, 508896, 524160, 635040, 648000, 648000, 657720, 673920, 725760, 761400, 833280, 890568, 939600

Offset: 1

Timothy L. Tiffin, Jul 22 2016

nonn

Each term represents the midpoint of an interval (x,y), where x (A260086) and y (A260087) form a pair of amicable numbers (A259933).  The length and radius of each interval can be found in A275469 and A275470, respectively.
This sequence is monotonic (specifically, nondecreasing), since x+y (A259953) is nondecreasing.  For a nonmonotonic ordering of these averages, see A275315.
It is unknown if there exists an amicable pair where x and y have opposite parity (one is even and the other is odd).  If such a pair is ever found, then the compound adjective "same-parity" will need to be added to the name of this sequence.

			a(  1) = (     220 +      284)/2 =      504/2 =      252.
a(  2) = (    1184 +     1210)/2 =     2394/2 =     1197.
a(  3) = (    2620 +     2924)/2 =     5544/2 =     2772.
...      ...                 ...          ...         ...
a(  9) = (   66928 +    66992)/2 =   133920/2 =    66960.
a( 10) = (   67095 +    71145)/2 =   138240/2 =    69120.
a( 11) = (   63020 +    76084)/2 =   139104/2 =    69552.
...      ...                 ...          ...         ...
a( 15) = (  122368 +   123152)/2 =   245520/2 =   122760.
a( 16) = (  122265 +   139815)/2 =   262080/2 =   131040.
a( 17) = (  141664 +   153176)/2 =   294840/2 =   147420.
...      ...                 ...          ...         ...
a( 32) = (  609928 +   686072)/2 =  1296000/2 =   648000.
a( 33) = (  643336 +   652664)/2 =  1296000/2 =   648000.
...      ...                 ...          ...         ...
a(107) = ( 9478910 + 11049730)/2 = 20528640/2 = 10264320.
a(108) = (10254970 + 10273670)/2 = 20528640/2 = 10264320.
...      ...                 ...          ...         ...
a(139) = (17754165 + 19985355)/2 = 37739520/2 = 18869760.
a(140) = (17844255 + 19895265)/2 = 37739520/2 = 18869760.
...      ...                 ...          ...         ...

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..142 from Timothy L. Tiffin)
VaxaSoftware, List of amicable numbers from 1 to 20,000,000 [142 pairs].

Cf. A260086, A260087, A259180, A259933, A259953, A275315, A275469, A275470.

With[{s = PositionIndex@ Array[DivisorSigma[1, #] &, 10^6]}, Flatten@ Map[Mean, Apply[Join, Map[Function[n, Select[Subsets[Lookup[s, n], {2}], Total@ # == n &]], Sort@ Select[Keys@ s, Length@ Lookup[s, #] > 1 &]]]]] (* Michael De Vlieger, Oct 22 2017 *)

a(n) = [A260086(n) + A260087(n)]/2 = A259953(n)/2.

A275469 Difference between the larger and smaller terms of the n-th amicable pair (x,y) given in A259933.

Original entry on oeis.org

64, 26, 304, 544, 136, 112, 2310, 1120, 64, 4050, 13064, 18018, 8980, 23670, 784, 17550, 11512, 26420, 4480, 4576, 18064, 5720, 84544, 81304, 110852, 43184, 17888, 17150, 11680, 3510, 69296, 76144, 9328, 67072, 76592, 115592, 70592, 61110, 21712, 82768

Offset: 1

Timothy L. Tiffin, Jul 28 2016

nonn

Each term represents the length of an interval (x,y), where x (A260086) and y (A260087) form a pair of amicable numbers (A259933).  The midpoint and radius of each interval can be found in A275316 and A275470, respectively.
Each term will be even as long as there does not exist an amicable pair where x and y have opposite parity.
This sequence is a rearrangement of A066539 (which is based on A002025, A002046, and A259180).  The first ten indices for which a(n) does not equal A066539(n) are n = 9, 10, 11, 15, 16, 33, 34, 35, 41, 42.

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

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].

Cf. A002025, A002046, A066539, A259180, A259933, A260086, A260087, A275316, A275470.

a(n) = A260087(n) - A260086(n).

cp's OEIS Frontend

A275316 Average of amicable pairs (x,y), ordered by the sum x+y given in A259953.

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