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

1,1

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