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# D.Series of $$\sigma$$

What is special about the sequence below ?

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

1 year, 5 months ago

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

Go further .... Try with sigma_3 · 1 year, 4 months ago

Can you actually find 8505000 or 8505? · 1 year, 4 months ago

It will give odd zeta which is what you do not what as they are irreducable · 1 year, 4 months ago

Sorry not with odd zetas try with even zetas andbakso change power of n with change in sigma_x · 1 year, 4 months ago

That will give odd zetas · 1 year, 4 months ago

Yes you are right Joel. · 1 year, 4 months ago

I see the pattern · 1 year, 4 months ago

Is a geometric progression with reason 10 · 1 year, 4 months ago

Next number 85050000. @Chinmay Sangawadekar · 1 year, 5 months ago

Not in that sense . · 1 year, 5 months ago

Then, what is the next number? · 1 year, 5 months ago

I think your number is correct , but i want its speciality · 1 year, 5 months ago

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

nope it is related to Dirichlet series . · 1 year, 5 months ago

Something related to zeta as the sigma is the divisor function · 1 year, 5 months ago