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Totient summatory function

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The totient summatory function (partial sums of Euler's totient function) is

where is Euler's totient function.


where is Euler's totient summatory function (A002088)
20204  


    

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| 375*58/20204 |
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px; bottom: 0; width: 4px; margin: 0 0 0 0; z-index: 0;"></div>
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px; bottom: 0; width: 4px; margin: 0 0 0 0; z-index: 0;"></div>
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px; bottom: 0; width: 4px; margin: 0 0 0 0; z-index: 0;"></div>
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px; bottom: 0; width: 4px; margin: 0 0 0 0; z-index: 0;"></div>
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0  

Asymptotic behavior

More precisely,

(A. Walfisz 1963)[1]Benoit Cloitre, Feb 02 2003

Is there a relation with the asymptotic behavior of the summatory quadratfrei function or is it a coincidence? (Cf. Talk:Totient summatory function#Asymptotic behavior of totient summatory function.)

Sequences

The totient summatory function (partial sums of Euler's totient function) (Cf. A092249 and A002088 for ) gives (all values for are even)

{1, 2, 4, 6, 10, 12, 18, 22, 28, 32, 42, 46, 58, 64, 72, 80, 96, 102, 120, 128, 140, 150, 172, 180, 200, 212, 230, 242, 270, 278, 308, 324, 344, 360, 384, 396, 432, 450, 474, 490, 530, 542, 584, 604, 628, ...}

Notes

  1. A. Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin 1963.