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The terms represent differences between consecutive amicable pair averages given in A275316.

Interestingly, the first two odd abundant numbers begin this sequence: a(1) = 945 = A005231(1) and a(2) = 1575 = A005231(2).

Of the first 141 terms, 4 are odd, 137 are even, 136 are abundant, 2 are deficient [specifically, a(27) = 31203 and a(28) = 31293], 7 numbers occur twice [specifically, a(53) = a(59) = 1728, a(25) = a(136) = 3024, a(21) = a(127) = 5184, a(31) = a(137) = 12960, a(34) = a(41) = 16200, a(74) = a(77) = 20736, and a(66) = a(104) = 156240], 3 numbers occur three times [specifically, a(32) = a(107) = a(139) = 0, a(35) = a(42) = a(52) = 51840, and a(30) = a(86) = a(97) = 110880], and every number is divisible by 3.

a(n) = A275066(n) for 41 of the first 141 indices: n = 1, 2, 3, 4, 5, 6, 7, 12, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 43, 44, 48, 49, 50, 57, 58, 59, 64, 65, 95, 120, 121.

a(n) = -A275066(n) for 9 of the first 141 indices: n = 15, 41, 46, 55, 67, 70, 81, 86, 141.

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.

Each term represents the length of an interval (x,y), where x (A260086) and y (A260087) form a pair of amicable numbers (A259933). The midpoint and radius of each interval can be found in A275316 and A275470, respectively.

Each term will be even as long as there does not exist an amicable pair where x and y have opposite parity.

This sequence is a rearrangement of A066539 (which is based on A002025, A002046, and A259180). The first ten indices for which a(n) does not equal A066539(n) are n = 9, 10, 11, 15, 16, 33, 34, 35, 41, 42.

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.