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%I #38 Apr 16 2021 04:34:02
%S 945,1575,2520,1008,4500,2640,4416,51696,-2592,2160,9504,5616,28080,
%T 18720,-8280,24660,8100,18576,4464,15840,5184,123228,26460,25704,3024,
%U 68400,31203,31293,15264,110880,12960,9720,16200,-25920,77760,35640,71880,57288,49032,97200
%N First differences of A275315.
%C The terms represent differences between consecutive amicable pair averages given in A275315.
%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, 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.
%C 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.
%C a(n) = -A275472(n) for 9 of the first 141 indices: n = 15, 41, 46, 55, 67, 70, 81, 86, 141.
%H Amiram Eldar, <a href="/A275066/b275066.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..141 from Timothy L. Tiffin)
%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) = A275315(n+1) - A275315(n).
%e a(9) = A275315(10) - A275315(9) = 66960 - 69552 = -2592.
%Y Cf. A002025, A002046, A005231, A259180, A275315, A275472.
%K sign
%O 1,1
%A _Timothy L. Tiffin_, Jul 29 2016
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