# D.Series of $$\sigma$$

What is special about the sequence below ?

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

2 years, 1 month ago

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

- 2 years ago

Go further .... Try with sigma_3

- 2 years ago

Can you actually find 8505000 or 8505?

- 2 years ago

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

- 2 years ago

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

- 2 years ago

That will give odd zetas

- 2 years ago

Yes you are right Joel.

- 2 years ago

I see the pattern

- 2 years ago

Is a geometric progression with reason 10

- 2 years ago

- 2 years, 1 month ago

Not in that sense .

- 2 years, 1 month ago

Then, what is the next number?

- 2 years, 1 month ago

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

- 2 years, 1 month ago

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

- 2 years, 1 month ago

nope it is related to Dirichlet series .

- 2 years, 1 month ago

Something related to zeta as the sigma is the divisor function

- 2 years, 1 month ago

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

- 2 years, 1 month ago

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