[seqfan] Re: Square Friendly Number

[Charles Greathouse]

Sure, here are some examples of x, y:
326 407
406 489
627 749
740 878
888 1102
1026 1208
880 1451
1284 1528
1528 1605
1628 1630
1510 1809
1110 1943
1956 2030
2013 2557
2072 3097
2996 3135
3216 3730
2508 3745
3260 4829
4866 4880
3912 6061
5064 6172
4946 6341
5829 7067
5064 7715
7248 10071
10065 10228
10536 11020
10360 12388
8052 12785
13066 14001
14248 14288
11836 14397
14397 14795
15544 15836
9768 17441
12122 17441
10686 17531
15504 19784
15544 19795
15000 20396
15430 22577
13398 24161
19560 24244
13986 24613
24717 24814
15000 25495
18582 27713
28268 29145
18678 30959
23316 35335
28770 37136
22470 39919
36240 40284
39864 40446
29414 43751
29046 45071
36141 46861
45689 48583

I've kept only the interesting pairs, that is, at most of one of p^e || x
and p^e || y (where p^e || n means p^e divides n and p^(e+1) does not
divide n). This is a weaker condition than being relatively prime (though I
think it's the right one for the problem), but in any case many/most of
these are relatively prime too.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Mon, Feb 3, 2014 at 10:44 PM, <zbi74583.boat at orange.zero.jp> wrote:

>     Hi,Seqfans
>
>     I asked about "Square Friendly Number" to Michel Murcus.
>
>     Sigma(x^2)=Sigma(y^2)
>
>     He sent me the result which he computed.
>
>     These are all k*4,k*5.
>     If a term which is essentially different from 4,5 exists  then it is
> interesting
>
>     I wonder if 2^4,5^2 is the only one solution of the following
>
>     Sigma(x^2)=Sigma(y^2), GCD(x,y)=1
>
>     Could anyone tell me if the other term exist?
>
>
>
>     Yasutoshi
>
>
>
>
>
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