A072160 Numerator of Sum_{k=1..n} phi(k)/k^4.

1, 17, 1409, 11353, 7137097, 7147097, 17199059897, 137714029801, 3721352084627, 3722696337299, 54537603391194659, 54547094712264659, 1558510008178113485699, 1558729492839246365699, 1558951562903235322883, 12472984853932601449939

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..585

Example

1, 17/16, 1409/1296, 11353/10368, 7137097/6480000, 7147097/6480000, ...

Maple

with(numtheory); seq(numer(add(phi(k)/k^4, k = 1..n)), n = 1..25); # G. C. Greubel, Aug 26 2019

Mathematica

Table[Numerator[Sum[EulerPhi[k]/k^4, {k, n}]], {n, 25}] (* G. C. Greubel, Aug 26 2019 *)
Accumulate[Table[EulerPhi[n]/n^4, {n, 20}]]//Numerator (* Harvey P. Dale, Nov 15 2020 *)

Prog

(PARI) a(n) = numerator(sum(k=1, n, eulerphi(k)/k^4)); \\ G. C. Greubel, Aug 26 2019
(Magma) [Numerator( &+[EulerPhi(k)/k^4: k in [1..n]] ): n in [1..25]]; // G. C. Greubel, Aug 26 2019
(Sage) [numerator( sum(euler_phi(k)/k^4 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^4) ) ); # G. C. Greubel, Aug 26 2019

Crossrefs

Cf. A072161.

Sequence in context: A203229 A269791 A256020 * A078814 A242282 A129911

Adjacent sequences: A072157 A072158 A072159 * A072161 A072162 A072163

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 28 2002

Status

approved