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
Examples
1, 3/2, 13/6, 8/3, 52/15, 19/5, 163/35, 361/70, 1223/210, ...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
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GAP
List([1..35], n-> DenominatorRat( Sum([1..n], k-> Phi(k)/k) ) ); # G. C. Greubel, Aug 25 2019
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Magma
[Denominator( &+[EulerPhi(k)/k: k in [1..n]] ): n in [1..35]]; // G. C. Greubel, Aug 25 2019
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Maple
with(numtheory); seq(denom( add(phi(k)/k, k=1..n)), n =1..35); # G. C. Greubel, Aug 25 2019
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Mathematica
Table[Sum[EulerPhi[k]/k,{k,n}],{n,40}]//Denominator (* Harvey P. Dale, Jun 08 2017 *) -
PARI
a(n) = denominator(sum(k=1, n, eulerphi(k)/k)); \\ Michel Marcus, Jan 26 2015
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Sage
[denominator( sum(euler_phi(k)/k for k in (1..n)) ) for n in (1..35)] # G. C. Greubel, Aug 25 2019
Formula
Also denominator of Sum_{i=1..n} (mu(i)/i)*floor(n/i). - Ridouane Oudra, Nov 26 2019