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#41 by Michael De Vlieger at Fri Nov 17 11:21:42 EST 2023
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#40 by Michel Marcus at Fri Nov 17 10:42:15 EST 2023
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#39 by Amiram Eldar at Fri Nov 17 09:36:06 EST 2023
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#38 by Amiram Eldar at Fri Nov 17 09:33:54 EST 2023
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| FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/3 = 1.0471975... (A019670).). - _Amiram Eldar_, Nov 17 2023
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#37 by Amiram Eldar at Fri Nov 17 09:25:39 EST 2023
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| FORMULA
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From Michael Somos, Jul 30 2006: (Start)
Moebius transform is period 12 sequence [1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, ...]. - _Michael Somos_, Jul 30 2006, ...].
Multiplicative with a(2^e) = a(3^e) = 1, a(p^e) = e+1 if p == 1(mod 4), a(p^e) = (1 + (-1)^e) / 2 if p == 3(mod 4). - _Michael Somos_, Jul 30 2006). (End)
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#36 by Amiram Eldar at Fri Nov 17 09:24:26 EST 2023
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| REFERENCES
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B. Bruce C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, 1994, see p. 197, Entry 44.
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#35 by Amiram Eldar at Fri Nov 17 09:23:43 EST 2023
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#34 by Alois P. Heinz at Tue Nov 06 19:11:34 EST 2018
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#33 by Andrew Howroyd at Tue Nov 06 18:36:33 EST 2018
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#32 by Andrew Howroyd at Tue Nov 06 14:13:59 EST 2018
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| FORMULA
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Dirichlet g.f.: zeta(s) * L(chi,s) where chi(n) = Kronecker( -36, n). Sum_{n>0} a(n) / n^s = Product_{p prime} 1 / ((1 - p^-s) * (1 - Kronecker( -36, p) * p^-s)). - Michael Somos, Jun 24 2011 */
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| STATUS
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approved
editing
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