A072159 Denominator of Sum_{k=1..n} phi(k)/k^3.

1, 8, 216, 864, 108000, 12000, 4116000, 16464000, 1333584000, 1333584000, 1775000304000, 1775000304000, 3899675667888000, 3899675667888000, 3899675667888000, 15598702671552000, 76636426225334976000, 2838386156493888000, 19468490647391577792000, 19468490647391577792000

Offset: 1

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• frac

Examples

			1, 9/8, 259/216, 1063/864, 136331/108000, 15259/12000, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..770

Crossrefs

Cf. A000010, A072158.

Programs

GAP

List([1..25], n-> DenominatorRat( Sum([1..n], k-> Phi(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

Maple

with(numtheory); seq(denom(add(phi(k)/k^3, k = 1..n)), n = 1..25); # G. C. Greubel, Aug 26 2019

Mathematica

Table[Denominator[Sum[EulerPhi[k]/k^3, {k, n}]], {n, 25}] (* G. C. Greubel, Aug 26 2019 *)
Denominator[Accumulate[Table[EulerPhi[k]/k^3, {k, 1, 30}]]] (* Amiram Eldar, Dec 28 2024 *)

PARI

a(n) = denominator( sum(k=1, n, eulerphi(k)/k^3)); \\ 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