A069220 Denominator of Sum_{1<=k<=n, gcd(k,n)=1} 1/k.

1, 1, 2, 3, 12, 5, 20, 105, 280, 63, 2520, 385, 27720, 6435, 8008, 45045, 720720, 85085, 4084080, 2909907, 3695120, 1322685, 5173168, 37182145, 118982864, 128707425, 2974571600, 717084225, 80313433200, 215656441, 2329089562800

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), Apr 12 2002

Keywords

• nonn
• frac

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..2310

Crossrefs

Cf. A017666, A002805.

Cf. A093600 (numerator of this sum).

Also denominators of row sums of A111879/A111880. For the numerators see A111881.

Programs

Mathematica

Table[s=0; Do[If[GCD[i, n]==1, s=s+1/i], {i, n}]; Denominator[s], {n, 1, 35}]
Table[Denominator[Total[1/Select[Range[n],GCD[n,#]==1&]]],{n,40}] (* Harvey P. Dale, Jun 07 2020 *)

PARI

for(n=1,40,print1(denominator(sum(k=1,n,if(gcd(k,n)==1,1/k))),","))

Formula

G.f. A(x) (for fractions) satisfies: A(x) = -log(1 - x)/(1 - x) - Sum_{k>=2} A(x^k)/k. - Ilya Gutkovskiy, Mar 31 2020

Extensions

More terms from Jason Earls, Apr 14 2002