A069947 Denominator of Sum_{k=1..n} k/phi(k).

1, 1, 2, 2, 4, 4, 12, 12, 12, 12, 60, 60, 10, 30, 120, 120, 240, 240, 720, 720, 720, 720, 7920, 7920, 7920, 7920, 7920, 7920, 55440, 55440, 11088, 11088, 55440, 55440, 55440, 55440, 18480, 55440, 55440, 55440, 55440, 55440, 55440, 11088, 11088, 11088, 255024, 255024

Offset: 1

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• frac

Examples

			1, 3, 9/2, 13/2, 31/4, 43/4, 143/12, 167/12, 185/12, ...
		

References

• József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 29, section I.27.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068885 (numerators), A028415, A048049.

Programs

Maple

map(denom, ListTools:-PartialSums([seq(n/numtheory:-phi(n),n=1..100)]));
# Robert Israel, May 01 2018

Mathematica

Accumulate[Table[n/EulerPhi[n],{n,50}]]//Denominator (* Harvey P. Dale, May 24 2021 *)

PARI

a(n) = denominator(sum(k = 1, n, k/eulerphi(k))); \\ Amiram Eldar, Apr 25 2024