A275066 First differences of A275315.

945, 1575, 2520, 1008, 4500, 2640, 4416, 51696, -2592, 2160, 9504, 5616, 28080, 18720, -8280, 24660, 8100, 18576, 4464, 15840, 5184, 123228, 26460, 25704, 3024, 68400, 31203, 31293, 15264, 110880, 12960, 9720, 16200, -25920, 77760, 35640, 71880, 57288, 49032, 97200

Offset: 1

Author

Timothy L. Tiffin, Jul 29 2016

Keywords

• sign

Comments

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.

Examples

			a(9) = A275315(10) - A275315(9) = 66960 - 69552 = -2592.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..141 from Timothy L. Tiffin)
• VaxaSoftware, List of amicable numbers from 1 to 20,000,000 [142 pairs].

Crossrefs

Cf. A002025, A002046, A005231, A259180, A275315, A275472.

Formula

a(n) = A275315(n+1) - A275315(n).