A072156 Numerator of Sum_{k=1..n} phi(k)/k^2.

1, 5, 53, 115, 3163, 3263, 170687, 352399, 1096397, 223513, 28103473, 28459213, 4963286677, 5029541437, 25532475569, 51741301813, 15299527769557, 15415359085157, 5677532668504877, 1144538596366201, 1156827116999161, 1166157760248361, 626832724103131129

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. A000010, A072157.

Cf. A001620, A013661, A306016.

Programs

GAP

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

Magma

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

Maple

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

Mathematica

Numerator[Table[Sum[EulerPhi[k]/k^2,{k,n}],{n,30}]] (* Vincenzo Librandi, Nov 15 2011 *)
Numerator[Accumulate[Table[EulerPhi[k]/k^2, {k, 1, 30}]]] (* Amiram Eldar, Dec 28 2024 *)

PARI

a(n) = numerator( sum(k=1,n, eulerphi(k)/k^2));
vector(25, n, a(n)) \\ G. C. Greubel, Aug 25 2019

Sage

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

Formula

a(n)/A072157(n) ~ (log(n) + gamma - zeta'(2)/zeta(2)) / zeta(2), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 28 2024