cp's OEIS Frontend

A036471 Four numbers (a,b,c,d) with a 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.

%I A036471 #41 Feb 16 2025 08:32:37
%S A036471 3270960,3767400,4651920,4969440,5682600,5405400,6514200,6126120,
%T A036471 6126120,6320160,6977880,7013160,6819120,6966960,7706160,7731360,
%U A036471 7469280,7469280,8353800,8288280,8316000,9258480,9009000,10048500,9840600,9923760,9563400
%N A036471 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 A036471 The sequence also contains the numbers 342151462276356306033089201934180, 6060968760324025992586151577119760, 99321681620793716265605322618607680, 409974875795109961540320351530842460160
%C A036471 The corresponding terms of A036472 would be: 357033595420351636473024008945820, 6324595118874800417522139587040240, 103641752270593503616169255168272320, 427807038915744951493564658435688099840
%C A036471 The corresponding terms of A036473 would be: 410581874773947356773179298713756, 7273164638852781748553461862929392, 119186052791523004137585762140907456, 491969994791994923787572902146102915072
%C A036471 The corresponding terms of A036474 would be: 428440439768072020710436590182244, 7589516361605847224013448168942608, 124370139086960335154801021607188544, 513368596793092084536932368118163836928
%C A036471 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 A036471 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 A036471 Donovan Johnson, <a href="/A036471/b036471.txt">Table of n, a(n) for n = 1..2000</a>
%H A036471 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AmicableQuadruple.html">Amicable Quadruple</a>
%Y A036471 Cf. A036472, A036473, A036474, A116148.
%Y A036471 Cf. A125490 - A125492 and A137231 (amicable triples).
%Y A036471 Cf. A233553 for amicable 5-tuples.
%K A036471 nonn
%O A036471 1,1
%A A036471 _Yasutoshi Kohmoto_
%E A036471 The present first term was found by _Dean Hickerson_, Nov 06 2006
%E A036471 That this is the first term was confirmed by _Giovanni Resta_, Nov 14 2006, who also found a(2)-a(18).
%E A036471 Edited by _N. J. A. Sloane_, Nov 07 2006 and Nov 27 2006