cp's OEIS Frontend

The terms represent differences between consecutive amicable pair averages given in A275315.

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, 104 are positive, 36 are negative, 1 is zero [specifically, a(137) = 0], 4 are odd, 137 are even, 138 have an absolute value that is an abundant number, 2 are deficient numbers [specifically, a(27) = 31203 and a(28) = 31293], 2 numbers occur twice [specifically, a(52) = a(59) = 1728 and a(30) = a(100) = 110880], and every number is divisible by 3.

a(n) = A275472(n) for 41 of the first 141 terms: 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) = -A275472(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 (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.