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A072158
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Numerator of Sum_{k=1..n} phi(k)/k^3.
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2
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1, 9, 259, 1063, 136331, 15259, 5305837, 21351973, 1740485813, 1745820149, 2337022458319, 2341131255319, 5164765371583843, 5173292359195843, 5182536034853059, 20760610355567611, 102246457919648504843, 3789825999242633809, 26045507479622115279931, 26064975970269506857723
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1, 9/8, 259/216, 1063/864, 136331/108000, 15259/12000, ...
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MAPLE
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with(numtheory); seq(numer(add(phi(k)/k^3, k = 1..n)), n = 1..25); # G. C. Greubel, Aug 26 2019
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MATHEMATICA
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Numerator[Table[Sum[EulerPhi[k]/k^3, {k, n}], {n, 20}]] (* Harvey P. Dale, May 27 2012 *)
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PROG
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(PARI) a(n) = numerator( sum(k=1, n, eulerphi(k)/k^3)); \\ G. C. Greubel, Aug 26 2019
(Magma) [Numerator( &+[EulerPhi(k)/k^3: k in [1..n]] ): n in [1..25]]; // G. C. Greubel, Aug 26 2019
(Sage) [numerator( sum(euler_phi(k)/k^3 for k in (1..n)) ) for n in (1..25)] # G. C. Greubel, Aug 26 2019
(GAP) List([1..25], n-> NumeratorRat( Sum([1..n], k-> Phi(k)/k^3) ) ); # G. C. Greubel, Aug 26 2019
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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