A072155 Denominator of Sum_{k=1..n} phi(k)/k.

1, 2, 6, 3, 15, 5, 35, 70, 210, 210, 2310, 770, 10010, 10010, 30030, 15015, 255255, 255255, 4849845, 4849845, 4849845, 4849845, 111546435, 37182145, 37182145, 37182145, 111546435, 111546435, 3234846615, 3234846615, 100280245065, 200560490130, 200560490130

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Also denominator of Sum_{i=1..n} (mu(i)/i)*floor(n/i). - Ridouane Oudra, Nov 26 2019

Example

1, 3/2, 13/6, 8/3, 52/15, 19/5, 163/35, 361/70, 1223/210, ...

Maple

with(numtheory); seq(denom( add(phi(k)/k, k=1..n)), n =1..35); # G. C. Greubel, Aug 25 2019

Mathematica

Table[Sum[EulerPhi[k]/k, {k, n}], {n, 40}]//Denominator (* Harvey P. Dale, Jun 08 2017 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, eulerphi(k)/k)); \\ Michel Marcus, Jan 26 2015
(Magma) [Denominator( &+[EulerPhi(k)/k: k in [1..n]] ): n in [1..35]]; // G. C. Greubel, Aug 25 2019
(Sage) [denominator( sum(euler_phi(k)/k for k in (1..n)) ) for n in (1..35)] # G. C. Greubel, Aug 25 2019
(GAP) List([1..35], n-> DenominatorRat( Sum([1..n], k-> Phi(k)/k) ) ); # G. C. Greubel, Aug 25 2019

Crossrefs

Cf. A071708 (numerators), A250031, A250032, A250034.

Sequence in context: A055773 A111866 A251753 * A094299 A304537 A330252

Adjacent sequences: A072152 A072153 A072154 * A072156 A072157 A072158

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 28 2002

Status

approved