A275472 - OEIS

%I #13 Aug 26 2016 23:06:13

%S 945,1575,2520,1008,4500,2640,4416,49104,2160,432,9072,5616,28080,

%T 10440,8280,16380,8100,18576,4464,15840,5184,123228,26460,25704,3024,

%U 68400,31203,31293,15264,110880,12960,0,9720,16200,51840,35640,71880,57288,49032,81000

%N First differences of A275316.

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

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

%C 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.

%C 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.

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

%H Timothy L. Tiffin, <a href="/A275472/b275472.txt">Table of n, a(n) for n = 1..141</a>

%H VaxaSoftware, <a href="http://www.vaxasoftware.com/doc_eduen/mat/numamigos_eng.pdf">List of amicable numbers from 1 to 20,000,000</a> [142 pairs].

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

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

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

%K nonn

%O 1,1

%A _Timothy L. Tiffin_, Jul 29 2016