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A072159
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Denominator of Sum_{k=1..n} phi(k)/k^3.
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2
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1, 8, 216, 864, 108000, 12000, 4116000, 16464000, 1333584000, 1333584000, 1775000304000, 1775000304000, 3899675667888000, 3899675667888000, 3899675667888000, 15598702671552000, 76636426225334976000, 2838386156493888000, 19468490647391577792000, 19468490647391577792000
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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(denom(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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Table[Denominator[Sum[EulerPhi[k]/k^3, {k, n}]], {n, 25}] (* G. C. Greubel, Aug 26 2019 *)
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PROG
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(PARI) a(n) = denominator( sum(k=1, n, eulerphi(k)/k^3)); \\ G. C. Greubel, Aug 26 2019
(Magma) [Denominator( &+[EulerPhi(k)/k^3: k in [1..n]] ): n in [1..25]]; // G. C. Greubel, Aug 26 2019
(Sage) [denominator( 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-> DenominatorRat( 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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