A072155 - OEIS

%I #20 Sep 08 2022 08:45:06

%S 1,2,6,3,15,5,35,70,210,210,2310,770,10010,10010,30030,15015,255255,

%T 255255,4849845,4849845,4849845,4849845,111546435,37182145,37182145,

%U 37182145,111546435,111546435,3234846615,3234846615,100280245065,200560490130,200560490130

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

%H G. C. Greubel, <a href="/A072155/b072155.txt">Table of n, a(n) for n = 1..1000</a>

%F Also denominator of Sum_{i=1..n} (mu(i)/i)*floor(n/i). - _Ridouane Oudra_, Nov 26 2019

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

%p with(numtheory); seq(denom( add(phi(k)/k, k=1..n)), n =1..35); # _G. C. Greubel_, Aug 25 2019

%t Table[Sum[EulerPhi[k]/k,{k,n}],{n,40}]//Denominator (* _Harvey P. Dale_, Jun 08 2017 *)

%o (PARI) a(n) = denominator(sum(k=1, n, eulerphi(k)/k)); \\ _Michel Marcus_, Jan 26 2015

%o (Magma) [Denominator( &+[EulerPhi(k)/k: k in [1..n]] ): n in [1..35]]; // _G. C. Greubel_, Aug 25 2019

%o (Sage) [denominator( sum(euler_phi(k)/k for k in (1..n)) ) for n in (1..35)] # _G. C. Greubel_, Aug 25 2019

%o (GAP) List([1..35], n-> DenominatorRat( Sum([1..n], k-> Phi(k)/k) ) ); # _G. C. Greubel_, Aug 25 2019

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

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Jun 28 2002