# D.Series of $\sigma$

What is special about the sequence below ?

$8505 , 85050 , 850500 , 8505000 , ......$

Note by A Former Brilliant Member
4 years, 12 months ago

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All that i can see is your question and $\displaystyle \sum _{ n=1 }^{ \infty }{ \frac { { \sigma }_{ 2 }\left( n \right) }{ { n }^{ 6 } } } =\frac { { \pi }^{ 6 } }{ 945 } \times \frac { { \pi }^{ 4 } }{ 90 } =\frac { { \pi }^{ 10 } }{ 85050 }$

- 4 years, 10 months ago

Yes you are right Joel.

- 4 years, 10 months ago

Go further .... Try with sigma_3

- 4 years, 10 months ago

That will give odd zetas

- 4 years, 10 months ago

It will give odd zeta which is what you do not what as they are irreducable

- 4 years, 10 months ago

Sorry not with odd zetas try with even zetas andbakso change power of n with change in sigma_x

- 4 years, 10 months ago

Can you actually find 8505000 or 8505?

- 4 years, 10 months ago

- 4 years, 12 months ago

Not in that sense .

- 4 years, 12 months ago

Then, what is the next number?

- 4 years, 12 months ago

I think your number is correct , but i want its speciality

- 4 years, 12 months ago

no '0" after 5 in 1st...... 1 '0' after 5 in 2nd.....Therefore ans is 85050000.I did like this. :P

- 4 years, 12 months ago

nope it is related to Dirichlet series .

- 4 years, 12 months ago

Something related to zeta as the sigma is the divisor function

- 4 years, 11 months ago

You. Are right ... Dirichlet's series of sigma function...

- 4 years, 11 months ago

Is a geometric progression with reason 10

- 4 years, 11 months ago

I see the pattern

- 4 years, 10 months ago