login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072155 Denominator of Sum_{k=1..n} phi(k)/k. 7
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)