%I #41 Feb 16 2025 08:32:37

%S 3270960,3767400,4651920,4969440,5682600,5405400,6514200,6126120,

%T 6126120,6320160,6977880,7013160,6819120,6966960,7706160,7731360,

%U 7469280,7469280,8353800,8288280,8316000,9258480,9009000,10048500,9840600,9923760,9563400

%N Four numbers (a,b,c,d) with a<b<c<d that satisfy sigma(a) = sigma(b) = sigma(c) = sigma(d) = a+b+c+d are called an amicable quadruple. We order these quadruples according to the common value of sigma. The values of (a, b, c, d, sigma) are in (this sequence, A036472, A036473, A036474, A116148) respectively.

%C The sequence also contains the numbers 342151462276356306033089201934180, 6060968760324025992586151577119760, 99321681620793716265605322618607680, 409974875795109961540320351530842460160

%C The corresponding terms of A036472 would be: 357033595420351636473024008945820, 6324595118874800417522139587040240, 103641752270593503616169255168272320, 427807038915744951493564658435688099840

%C The corresponding terms of A036473 would be: 410581874773947356773179298713756, 7273164638852781748553461862929392, 119186052791523004137585762140907456, 491969994791994923787572902146102915072

%C The corresponding terms of A036474 would be: 428440439768072020710436590182244, 7589516361605847224013448168942608, 124370139086960335154801021607188544, 513368596793092084536932368118163836928

%C As stated, we first order by common sigma value. When the common value of sigma is the same for several quadruples, these are then sorted (ascending) by the smallest member. When the smallest members also agree, we go on to the second smallest members, and so on, lexicographically. - _Jeppe Stig Nielsen_, Feb 02 2015

%C Of the first 2000 quadruples, there are 78 cases where both the value of sigma, the value of the smallest member (a), and the value of the second smallest member (b) agree with those of the previous quadruple. The first time this happens is for n=17 and n=18 which correspond to the tuples (7469280, 8157240, 8873760, 9368520) and (7469280, 8157240, 9098460, 9143820), respectively. - _Jeppe Stig Nielsen_, Feb 02 2015

%H Donovan Johnson, <a href="/A036471/b036471.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmicableQuadruple.html">Amicable Quadruple</a>

%Y Cf. A036472, A036473, A036474, A116148.

%Y Cf. A125490 - A125492 and A137231 (amicable triples).

%Y Cf. A233553 for amicable 5-tuples.

%K nonn,changed

%O 1,1

%A _Yasutoshi Kohmoto_

%E The present first term was found by _Dean Hickerson_, Nov 06 2006

%E That this is the first term was confirmed by _Giovanni Resta_, Nov 14 2006, who also found a(2)-a(18).

%E Edited by _N. J. A. Sloane_, Nov 07 2006 and Nov 27 2006