[seqfan] Re: sigma(odd square) = odd square

[Max Alekseyev]

Here are all odd squarefree numbers m such that the prime divisors of both
m and sigma(m^2) are below 300 and sigma(m^2) is an odd square.

[1, 247863, 469623, 985369, 1933815, 2181409, 14142695, 41193543, 52256985,
63355655, 78048903, 94799985, 22535428895, 53257909705, 100907111305,
100952955455, 135545609265, 245894816265, 449134850879, 814780591079,
1093974229257, 1905521352735, 2149492804921, 4218441445335, 4900724638953,
8851187928505, 16770237706105, 1164978366136871, 1743174017143377,
2113400373846671, 7808973582128433, 4156721428548303615]

If I increase the bound for prime divisors from 300 to 1000, then there are
2^16 = 65536 such numbers.

Regards,
Max


On Sat, Feb 13, 2016 at 3:13 PM, Zak Seidov <zakseidov at mail.ru> wrote:

>  Just found:
> sigma (1476326929 = 7^2*11^2*499^2) = 1891467081 = 3^2*7^2*19^2*109^2.
> Next one?
>
>
> >Суббота, 13 февраля 2016, 23:05 +03:00 от Zak Seidov <zakseidov at mail.ru>:
> >
> >
> >Are 1 and 81 the only odd squares with odd square sigma:
> >sigma(1)=1 and sigma(81)=121?
> >--
> >Zak  Seidov
> >
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