# [seqfan] Re: Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v

Richard Guy rkg at cpsc.ucalgary.ca
Thu Nov 27 17:13:00 CET 2008

```Neil,
Sorry for my stupidity.  In defence
I plead that the description might be
made a bit more RKG-proof.  When one

The values of a, b, c, d, sigma are in
this sequence, A036472, A036473,
A036474 and A116148 respectively.

(this) one tends to concentrate on
the four nice blue underlined sequence
numbers, and associate them respectively
with a, b, c, d, and ignore the
comparatively fine print of `sigma'
and `this sequence'.    R.

On Thu, 27 Nov 2008, N. J. A. Sloane wrote:

> On Nov 23 Richard Guy said:
>>                This discovery prompted me to look up
>> amicable triples & quadruples in OEIS.  For the former,
>> I found x, y, z, in A125490,1,2, but didn't find x+y+z.
>
> Me: x+y+z will be A137231 soon. I assume the definitions of A125490,1,2
> should be changed to read
> %N A125490 Amicable triples: numbers such that sigma(x) = sigma(y) = sigma(z) = x+y+z, x<y<z. Sequence gives x numbers.
> %N A125491 Amicable triples: numbers such that sigma(x) = sigma(y) = sigma(z) = x+y+z, x<y<z. Sequence gives y numbers.
> %N A125492 Amicable triples: numbers such that sigma(x) = sigma(y) = sigma(z) = x+y+z, x<y<z. Sequence gives z numbers.
> , right?  (The clause "= x+y+z" was missing)
>
>>                For [amicable quadruples], there's some confusion,
>> A036471,2,3,4  shd be a,b,c,d and A116148 a+b+c+d,
>> but there seems to be something wrong with the statements.
>
> Richard, Here are extracts from those 5 entries. What were the errors?
>
> %S A036471 3270960,3767400,4651920,4969440,5682600,5405400,6514200,6126120,
> %T A036471 6126120,6320160,6977880,7013160,6819120,6966960,7706160,7731360,
> %U A036471 7469280,7469280
> %N A036471 Four numbers (a,b,c,d) with a<b<c<d which 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 and A116148 respectively.
>
> %S A036472 3361680,4090320,4839120,5116320,5831280,6029100,6640200,6541920,
> %T A036472 6922080,6902280,7087080,7436520,7327320,7054320,7722000,7852320,
> %U A036472 8157240,8157240
> %N A036472 Amicable quadruples: the numbers b referred to in A036471.
>
> %S A036473 3461040,4150440,4918320,5475960,5920200,6421800,6768720,7559640,
> %T A036473 7280280,7685496,7227360,7688520,7715400,7840560,7948080,8125920,
> %U A036473 8873760,9098460
> %N A036473 Amicable quadruples: the numbers c referred to in A036471.
>
> %S A036474 3834000,4240800,5089392,5666760,6939360,7142100,7932240,8076960,
> %T A036474 7976160,8122464,7738080,7738920,8136240,8136240,9121680,9312480,
> %U A036474 9368520,9143820
> %N A036474 Amicable quadruples: the numbers d referred to in A036471.
>
> %S A116148 13927680,16248960,19498752,21228480,24373440,24998400,27855360,
> %T A116148 28304640,28304640,29030400,29030400,29877120,29998080,29998080,
> %U A116148 32497920,33022080,33868800,33868800
> %N A116148 Amicable quadruples: the values of sigma corresponding to A036471-A036474.
> %C A116148 Note that repetitions occur.
>
> Best regards,  Neil
>
>
>
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```