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A275316 Average of amicable pairs (x,y), ordered by the sum x+y given in A259953. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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].

FORMULA

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

EXAMPLE

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.

...      ...                 ...          ...         ...

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A250794 A245858 A200884 * A275315 A184505 A184499

Adjacent sequences:  A275313 A275314 A275315 * A275317 A275318 A275319

KEYWORD

nonn

AUTHOR

Timothy L. Tiffin, Jul 22 2016

STATUS

approved

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Last modified September 27 07:01 EDT 2022. Contains 357052 sequences. (Running on oeis4.)