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D.Series of \(\sigma\)

What is special about the sequence below ?

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

Note by Chinmay Sangawadekar
7 months, 3 weeks ago

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

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@Joel Yip Go further .... Try with sigma_3 Chinmay Sangawadekar · 6 months, 2 weeks ago

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@Chinmay Sangawadekar Can you actually find 8505000 or 8505? Joel Yip · 6 months, 2 weeks ago

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@Chinmay Sangawadekar It will give odd zeta which is what you do not what as they are irreducable Joel Yip · 6 months, 2 weeks ago

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@Joel Yip Sorry not with odd zetas try with even zetas andbakso change power of n with change in sigma_x Chinmay Sangawadekar · 6 months, 2 weeks ago

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@Chinmay Sangawadekar That will give odd zetas Joel Yip · 6 months, 2 weeks ago

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@Joel Yip Yes you are right Joel. Chinmay Sangawadekar · 6 months, 2 weeks ago

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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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@Abhay Kumar Not in that sense . Chinmay Sangawadekar · 7 months, 3 weeks ago

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@Chinmay Sangawadekar Then, what is the next number? Abhay Kumar · 7 months, 3 weeks ago

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@Abhay Kumar I think your number is correct , but i want its speciality Chinmay Sangawadekar · 7 months, 3 weeks ago

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@Chinmay Sangawadekar no '0" after 5 in 1st...... 1 '0' after 5 in 2nd.....Therefore ans is 85050000.I did like this. :P Abhay Kumar · 7 months, 3 weeks ago

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@Abhay Kumar nope it is related to Dirichlet series . Chinmay Sangawadekar · 7 months, 3 weeks ago

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@Chinmay Sangawadekar Something related to zeta as the sigma is the divisor function Joel Yip · 7 months, 2 weeks ago

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@Joel Yip You. Are right ... Dirichlet's series of sigma function... Chinmay Sangawadekar · 7 months, 2 weeks ago

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