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.

3270960, 3767400, 4651920, 4969440, 5682600, 5405400, 6514200, 6126120, 6126120, 6320160, 6977880, 7013160, 6819120, 6966960, 7706160, 7731360, 7469280, 7469280, 8353800, 8288280, 8316000, 9258480, 9009000, 10048500, 9840600, 9923760, 9563400

Offset

1,1

Comments

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

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

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

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

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

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

Links

Donovan Johnson, Table of n, a(n) for n = 1..2000

Eric Weisstein's World of Mathematics, Amicable Quadruple

Crossrefs

Cf. A036472, A036473, A036474, A116148.

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

Cf. A233553 for amicable 5-tuples.

Sequence in context: A357755 A217110 A217111 * A206316 A186959 A369897

Adjacent sequences: A036468 A036469 A036470 * A036472 A036473 A036474

Keyword

nonn

Author

Yasutoshi Kohmoto

Extensions

The present first term was found by Dean Hickerson, Nov 06 2006

That this is the first term was confirmed by Giovanni Resta, Nov 14 2006, who also found a(2)-a(18).

Edited by N. J. A. Sloane, Nov 07 2006 and Nov 27 2006

Status

approved