A072157 Denominator of Sum_{k=1..n} phi(k)/k^2.

1, 4, 36, 72, 1800, 1800, 88200, 176400, 529200, 105840, 12806640, 12806640, 2164322160, 2164322160, 10821610800, 21643221600, 6254891042400, 6254891042400, 2258015666306400, 451603133261280, 451603133261280, 451603133261280, 238898057495217120, 238898057495217120

Offset: 1

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• frac

Examples

			1, 5/4, 53/36, 115/72, 3163/1800, 3263/1800, 170687/88200, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A072156.

Programs

GAP

List([1..25], n-> DenominatorRat( Sum([1..n], k-> Phi(k)/k^2) ) ); # G. C. Greubel, Aug 26 2019

Magma

[Denominator( &+[EulerPhi(k)/k^2: k in [1..n]] ): n in [1..25]]; // G. C. Greubel, Aug 26 2019

Maple

with(numtheory); seq(denom(add(phi(k)/k^2, k = 1..n)), n = 1..25); # G. C. Greubel, Aug 26 2019

Mathematica

Denominator[Table[Sum[EulerPhi[k]/k^2,{k,n}],{n,30}]] (* Harvey P. Dale, Nov 13 2011 *)
Accumulate[Table[EulerPhi[n]/n^2,{n,30}]]//Denominator (* More efficient than the first above program. *) (* Harvey P. Dale, Sep 19 2022 *)

PARI

a(n) = denominator( sum(k=1, n, eulerphi(k)/k^2)); \\ G. C. Greubel, Aug 26 2019

Sage

[denominator( sum(euler_phi(k)/k^2 for k in (1..n)) ) for n in (1..25)] # G. C. Greubel, Aug 26 2019