A162884 -id:A162884 - cp's OEIS frontend

A275315 Average of amicable pairs (x,y), ordered by the smaller value x given in A002025.

252, 1197, 2772, 5292, 6300, 10800, 13440, 17856, 69552, 66960, 69120, 78624, 84240, 112320, 131040, 122760, 147420, 155520, 174096, 178560, 194400, 199584, 322812, 349272, 374976, 378000, 446400, 477603, 508896, 524160, 635040, 648000, 657720, 673920, 648000, 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 (A002025) and y (A002046) form a pair of amicable numbers (A259180).  The length and radius of each interval can be found in A066539 and A162884, respectively.
This sequence is not monotonic (specifically, not nondecreasing), since x+y (A180164) is not monotonic.  For a monotonic (nondecreasing) ordering of these averages, see A275316.
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) = (   63020 +    76084)/2 =   139104/2 =    69552.
a( 10) = (   66928 +    66992)/2 =   133920/2 =    66960.
a( 11) = (   67095 +    71145)/2 =   138240/2 =    69120.
...      ...                 ...          ...         ...
a( 15) = (  122265 +   139815)/2 =   262080/2 =   131040.
a( 16) = (  122368 +   123152)/2 =   245520/2 =   122760.
a( 17) = (  141664 +   153176)/2 =   294840/2 =   147420.
...      ...                 ...          ...         ...
a( 32) = (  609928 +   686072)/2 =  1296000/2 =   648000.
...      ...                 ...          ...         ...
a( 35) = (  643336 +   652664)/2 =  1296000/2 =   648000.
...      ...                 ...          ...         ...
a(105) = ( 9478910 + 11049730)/2 = 20528640/2 = 10264320.
...      ...                 ...          ...         ...
a(109) = (10254970 + 10273670)/2 = 20528640/2 = 10264320.
...      ...                 ...          ...         ...
a(137) = (17754165 + 19985355)/2 = 37739520/2 = 18869760.
a(138) = (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. A002025, A002046, A066539, A162884, A180164, A259180, A275316.

a(n) = [A002025(n) + A002046(n)]/2 = A180164(n)/2.

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

Original entry on oeis.org

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

Timothy L. Tiffin, Jul 28 2016

nonn

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.

			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.

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, A260086, A260087, A162884, A259933, A275316, A275469.

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

cp's OEIS Frontend

A275315 Average of amicable pairs (x,y), ordered by the smaller value x given in A002025.

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