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What is special about the sequence below ?

\[8505 , 85050 , 850500 , 8505000 , ......\]

Note by A Brilliant Member 2 years, 7 months ago

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

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Go further .... Try with sigma_3

Can you actually find 8505000 or 8505?

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

@Joel Yip – Sorry not with odd zetas try with even zetas andbakso change power of n with change in sigma_x

That will give odd zetas

Yes you are right Joel.

I see the pattern

Is a geometric progression with reason 10

Next number 85050000. @Chinmay Sangawadekar

Not in that sense .

Then, what is the next number?

@Abhay Kumar – I think your number is correct , but i want its speciality

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

@Abhay Kumar – nope it is related to Dirichlet series .

@A Brilliant Member – Something related to zeta as the sigma is the divisor function

@Joel Yip – You. Are right ... Dirichlet's series of sigma function...

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## Comments

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

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Go further .... Try with sigma_3

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Can you actually find 8505000 or 8505?

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

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That will give odd zetas

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Yes you are right Joel.

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I see the pattern

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Is a geometric progression with reason 10

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Next number 85050000. @Chinmay Sangawadekar

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Not in that sense .

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Then, what is the next number?

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