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A275315 Average of amicable pairs (x,y), ordered by the smaller value x given in A002025. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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

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

CROSSREFS

Cf. A002025, A002046, A066539, A162884, A180164, A259180, A275316.

Sequence in context: A245858 A200884 A275316 * A184505 A184499 A154045

Adjacent sequences:  A275312 A275313 A275314 * A275316 A275317 A275318

KEYWORD

nonn

AUTHOR

Timothy L. Tiffin, Jul 22 2016

STATUS

approved

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Last modified October 2 20:53 EDT 2022. Contains 357230 sequences. (Running on oeis4.)