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A306613 First differences of A063990 (amicable numbers arranged in increasing order). 0
64, 900, 26, 1410, 304, 2096, 544, 668, 136, 4376, 112, 1429, 2310, 2701, 1120, 44604, 3908, 64, 103, 2520, 1530, 4939, 3666, 7883, 1097, 11755, 21780, 103, 784, 1003, 15660, 1849, 646, 10866, 15554, 3126, 4416, 64, 4512, 4520, 11356, 5720, 988, 77108, 28080, 10930 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..46.

FORMULA

a(n) = A063990(n+1) - A063990(n). - Michel Marcus, Apr 08 2019

EXAMPLE

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

From Bernard Schott, Mar 10 2019: (Start)

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

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)

PROG

(MATLAB)

clear

clc

A = zeros(100000, 1);

parfor n = 1:1:100000

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

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

     A(n) = sum(f) - n;

end

D = [];

d = 1;

for a = 1:1:100000

    for b = 1:1:100000

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

            D(d) = a;

            d = d+1;

        end

    end

end

D

difference = diff(D)

CROSSREFS

Cf. A063990 (amicable numbers), A306612.

Cf. A002025, A002046.

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

Cf. A139228 (first differences of perfect numbers).

Sequence in context: A283547 A297686 A292028 * A185368 A027003 A265620

Adjacent sequences:  A306610 A306611 A306612 * A306614 A306615 A306616

KEYWORD

nonn

AUTHOR

Conor Coons, Feb 28 2019

EXTENSIONS

More terms from Michel Marcus, Mar 09 2019

STATUS

approved

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Last modified November 30 08:19 EST 2021. Contains 349419 sequences. (Running on oeis4.)