This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275316 #43 Oct 01 2020 03:16:05
%S A275316 252,1197,2772,5292,6300,10800,13440,17856,66960,69120,69552,78624,
%T A275316 84240,112320,122760,131040,147420,155520,174096,178560,194400,199584,
%U A275316 322812,349272,374976,378000,446400,477603,508896,524160,635040,648000,648000,657720,673920,725760,761400,833280,890568,939600
%N A275316 Average of amicable pairs (x,y), ordered by the sum x+y given in A259953.
%C A275316 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.
%C A275316 This sequence is monotonic (specifically, nondecreasing), since x+y (A259953) is nondecreasing. For a nonmonotonic ordering of these averages, see A275315.
%C 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.
%H A275316 Amiram Eldar, <a href="/A275316/b275316.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..142 from Timothy L. Tiffin)
%H A275316 VaxaSoftware, <a href="http://www.vaxasoftware.com/doc_eduen/mat/numamigos_eng.pdf">List of amicable numbers from 1 to 20,000,000</a> [142 pairs].
%F A275316 a(n) = [A260086(n) + A260087(n)]/2 = A259953(n)/2.
%e A275316 a( 1) = ( 220 + 284)/2 = 504/2 = 252.
%e A275316 a( 2) = ( 1184 + 1210)/2 = 2394/2 = 1197.
%e A275316 a( 3) = ( 2620 + 2924)/2 = 5544/2 = 2772.
%e A275316 ... ... ... ... ...
%e A275316 a( 9) = ( 66928 + 66992)/2 = 133920/2 = 66960.
%e A275316 a( 10) = ( 67095 + 71145)/2 = 138240/2 = 69120.
%e A275316 a( 11) = ( 63020 + 76084)/2 = 139104/2 = 69552.
%e A275316 ... ... ... ... ...
%e A275316 a( 15) = ( 122368 + 123152)/2 = 245520/2 = 122760.
%e A275316 a( 16) = ( 122265 + 139815)/2 = 262080/2 = 131040.
%e A275316 a( 17) = ( 141664 + 153176)/2 = 294840/2 = 147420.
%e A275316 ... ... ... ... ...
%e A275316 a( 32) = ( 609928 + 686072)/2 = 1296000/2 = 648000.
%e A275316 a( 33) = ( 643336 + 652664)/2 = 1296000/2 = 648000.
%e A275316 ... ... ... ... ...
%e A275316 a(107) = ( 9478910 + 11049730)/2 = 20528640/2 = 10264320.
%e A275316 a(108) = (10254970 + 10273670)/2 = 20528640/2 = 10264320.
%e A275316 ... ... ... ... ...
%e A275316 a(139) = (17754165 + 19985355)/2 = 37739520/2 = 18869760.
%e A275316 a(140) = (17844255 + 19895265)/2 = 37739520/2 = 18869760.
%e A275316 ... ... ... ... ...
%t A275316 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 *)
%Y A275316 Cf. A260086, A260087, A259180, A259933, A259953, A275315, A275469, A275470.
%K A275316 nonn
%O A275316 1,1
%A A275316 _Timothy L. Tiffin_, Jul 22 2016