A306613 - OEIS

%I #30 May 12 2019 08:32:11

%S 64,900,26,1410,304,2096,544,668,136,4376,112,1429,2310,2701,1120,

%T 44604,3908,64,103,2520,1530,4939,3666,7883,1097,11755,21780,103,784,

%U 1003,15660,1849,646,10866,15554,3126,4416,64,4512,4520,11356,5720,988,77108,28080,10930

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

%C a(n) is the difference between the n-th and (n+1)-th amicable numbers when ordered by increasing value.

%C 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 a(n) = A063990(n+1) - A063990(n). - _Michel Marcus_, Apr 08 2019

%e a(2) = amicable(3) - amicable(2) = 1184 - 284 = 900.

%e From _Bernard Schott_, Mar 10 2019: (Start)

%e a(1) = 284 - 220 = 64 is the difference between the larger and the smaller terms of the first amicable pair.

%e 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 (MATLAB)

%o clear

%o clc

%o A = zeros(100000,1);

%o parfor n = 1:1:100000

%o      f = find(rem(n, 1:floor(sqrt(n))) == 0);

%o      f = unique([1, n, f, fix(n./f)]);

%o      A(n) = sum(f) - n;

%o end

%o D = [];

%o d = 1;

%o for a = 1:1:100000

%o     for b = 1:1:100000

%o         if A(a) == b && A(b) == a && a~=b

%o             D(d) = a;

%o             d = d+1;

%o         end

%o     end

%o end

%o D

%o difference = diff(D)

%Y Cf. A063990 (amicable numbers), A306612.

%Y Cf. A002025, A002046.

%Y Cf. A066539 (difference between larger and smaller terms of n-th amicable pair).

%Y Cf. A139228 (first differences of perfect numbers).

%K nonn

%O 1,1

%A _Conor Coons_, Feb 28 2019

%E More terms from _Michel Marcus_, Mar 09 2019