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A306613 First differences of A063990 (amicable numbers arranged in increasing order).

%I A306613 #30 May 12 2019 08:32:11
%S A306613 64,900,26,1410,304,2096,544,668,136,4376,112,1429,2310,2701,1120,
%T A306613 44604,3908,64,103,2520,1530,4939,3666,7883,1097,11755,21780,103,784,
%U A306613 1003,15660,1849,646,10866,15554,3126,4416,64,4512,4520,11356,5720,988,77108,28080,10930
%N A306613 First differences of A063990 (amicable numbers arranged in increasing order).
%C A306613 a(n) is the difference between the n-th and (n+1)-th amicable numbers when ordered by increasing value.
%C A306613 For 1 <= k <= 8, a(2k-1) is the difference between the larger and the smaller terms of the k-th amicable pair, and for 1 <= k <= 8, a(2k) is the difference between the smaller term of the (k+1)-th pair and the larger term of the k-th pair. Beginning with the 9th pair (63020,76084), the pairs ordered by their first element are no longer adjacent. - _Bernard Schott_, Mar 09 2019
%F A306613 a(n) = A063990(n+1) - A063990(n). - _Michel Marcus_, Apr 08 2019
%e A306613 a(2) = amicable(3) - amicable(2) = 1184 - 284 = 900.
%e A306613 From _Bernard Schott_, Mar 10 2019: (Start)
%e A306613 a(1) = 284 - 220 = 64 is the difference between the larger and the smaller terms of the first amicable pair.
%e A306613 a(4) = 2620 - 1210 = 1410 is the difference between the smaller term of the third amicable pair and the larger term of the second amicable pair. (End)
%o A306613 (MATLAB)
%o A306613 clear
%o A306613 clc
%o A306613 A = zeros(100000,1);
%o A306613 parfor n = 1:1:100000
%o A306613      f = find(rem(n, 1:floor(sqrt(n))) == 0);
%o A306613      f = unique([1, n, f, fix(n./f)]);
%o A306613      A(n) = sum(f) - n;
%o A306613 end
%o A306613 D = [];
%o A306613 d = 1;
%o A306613 for a = 1:1:100000
%o A306613     for b = 1:1:100000
%o A306613         if A(a) == b && A(b) == a && a~=b
%o A306613             D(d) = a;
%o A306613             d = d+1;
%o A306613         end
%o A306613     end
%o A306613 end
%o A306613 D
%o A306613 difference = diff(D)
%Y A306613 Cf. A063990 (amicable numbers), A306612.
%Y A306613 Cf. A002025, A002046.
%Y A306613 Cf. A066539 (difference between larger and smaller terms of n-th amicable pair).
%Y A306613 Cf. A139228 (first differences of perfect numbers).
%K A306613 nonn
%O A306613 1,1
%A A306613 _Conor Coons_, Feb 28 2019
%E A306613 More terms from _Michel Marcus_, Mar 09 2019