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A319091
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Decimal expansion of D, the coefficient of n in the asymptotic formula of Ramanujan for Sum_{k=1..n} (d(k)^2), where d(k) is the number of distinct divisors of k.
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3
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4, 6, 0, 3, 2, 3, 3, 7, 2, 2, 5, 8, 7, 2, 1, 4, 3, 0, 3, 9, 3, 7, 6, 2, 0, 8, 6, 3, 8, 4, 4, 1, 8, 9, 7, 4, 7, 6, 3, 2, 1, 4, 9, 0, 3, 5, 3, 8, 7, 3, 9, 2, 2, 4, 0, 5, 8, 4, 2, 5, 0, 3, 4, 8, 4, 4, 5, 9, 0, 2, 6, 2, 9, 3, 2, 4, 0, 3, 2, 0, 7, 3, 8, 0, 1, 9, 8, 4, 8, 1, 0, 7, 6, 5, 9, 8, 5, 9, 9, 7, 3, 5, 6, 9, 5, 8
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OFFSET
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0,1
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LINKS
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FORMULA
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D = 24*gamma^3/Pi^2 - (432*z1 /Pi^4+ 36/Pi^2)*gamma^2 + (3456*z1^2/Pi^6 + 288*(z1-z2)/Pi^4 + 24/Pi^2 - 72*g1/Pi^2)*gamma + g1*(288*z1/Pi^4 + 24/Pi^2)-10368*z1^3/Pi^8 - 864*z1^2/Pi^6 + 1728*z2*z1/Pi^6 + 72*(z2-z1)/Pi^4- 48*z3/Pi^4 + (12*g2-6)/Pi^2, where gamma is the Euler-Mascheroni constant A001620, z1 = Zeta'(2) = A073002, z2 = Zeta''(2) = A201994, z3 = Zeta'''(2) = A201995 and g1, g2 are the Stieltjes constants, see A082633 and A086279.
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EXAMPLE
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0.4603233722587214303937620863844189747632149035387392240584250348445902629324...
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MATHEMATICA
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24*EulerGamma^3/Pi^2 - (432*Zeta'[2] /Pi^4+ 36/Pi^2)*EulerGamma^2 + (3456*Zeta'[2]^2/Pi^6 + 288*(Zeta'[2]-Zeta''[2])/Pi^4 + 24/Pi^2 - 72*StieltjesGamma[1]/Pi^2)*EulerGamma + StieltjesGamma[1]*(288*Zeta'[2]/Pi^4 + 24/Pi^2)-10368*Zeta'[2]^3/Pi^8 - 864*Zeta'[2]^2/Pi^6 + 1728*Zeta''[2] * Zeta'[2]/Pi^6 + 72*(Zeta''[2]-Zeta'[2])/Pi^4 - 48*Zeta'''[2]/Pi^4 + (12*StieltjesGamma[2] - 6)/Pi^2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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