A275472 First differences of A275316.

945, 1575, 2520, 1008, 4500, 2640, 4416, 49104, 2160, 432, 9072, 5616, 28080, 10440, 8280, 16380, 8100, 18576, 4464, 15840, 5184, 123228, 26460, 25704, 3024, 68400, 31203, 31293, 15264, 110880, 12960, 0, 9720, 16200, 51840, 35640, 71880, 57288, 49032, 81000

Offset

1,1

Comments

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.

Links

Timothy L. Tiffin, Table of n, a(n) for n = 1..141

VaxaSoftware, List of amicable numbers from 1 to 20,000,000 [142 pairs].

Formula

a(n) = A275316(n+1) - A275316(n).

Example

a(9) = A275316(10) - A275316(9) = 69120 - 66960 = 2160.

Crossrefs

Cf. A005231, A260086, A260087, A259933, A275066, A275316.

Sequence in context: A287646 A316116 A188439 * A275066 A127667 A252184

Adjacent sequences: A275469 A275470 A275471 * A275473 A275474 A275475

Keyword

nonn

Author

Timothy L. Tiffin, Jul 29 2016

Status

approved