What is special about the sequence below ?

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

What is special about the sequence below ?

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

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

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– Chinmay Sangawadekar · 6 months, 2 weeks ago

Go further .... Try with sigma_3Log in to reply

– Joel Yip · 6 months, 2 weeks ago

Can you actually find 8505000 or 8505?Log in to reply

– Joel Yip · 6 months, 2 weeks ago

It will give odd zeta which is what you do not what as they are irreducableLog in to reply

– Chinmay Sangawadekar · 6 months, 2 weeks ago

Sorry not with odd zetas try with even zetas andbakso change power of n with change in sigma_xLog in to reply

– Joel Yip · 6 months, 2 weeks ago

That will give odd zetasLog in to reply

– Chinmay Sangawadekar · 6 months, 2 weeks ago

Yes you are right Joel.Log in to reply

I see the pattern – Joel Yip · 6 months, 2 weeks ago

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Is a geometric progression with reason 10 – Kiyoshi Araki · 6 months, 3 weeks ago

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Next number 85050000. @Chinmay Sangawadekar – Abhay Kumar · 7 months, 3 weeks ago

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– Chinmay Sangawadekar · 7 months, 3 weeks ago

Not in that sense .Log in to reply

– Abhay Kumar · 7 months, 3 weeks ago

Then, what is the next number?Log in to reply

– Chinmay Sangawadekar · 7 months, 3 weeks ago

I think your number is correct , but i want its specialityLog in to reply

– Abhay Kumar · 7 months, 3 weeks ago

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

– Chinmay Sangawadekar · 7 months, 3 weeks ago

nope it is related to Dirichlet series .Log in to reply

– Joel Yip · 7 months, 2 weeks ago

Something related to zeta as the sigma is the divisor functionLog in to reply

– Chinmay Sangawadekar · 7 months, 2 weeks ago

You. Are right ... Dirichlet's series of sigma function...Log in to reply