A048049 Denominator of Sum_{k=1..n} 1/phi(k).

1, 1, 2, 1, 4, 4, 12, 6, 3, 12, 60, 15, 60, 60, 120, 30, 240, 80, 720, 720, 720, 720, 7920, 7920, 1584, 1584, 1584, 1584, 11088, 11088, 55440, 13860, 1386, 11088, 11088, 11088, 11088, 11088, 11088, 5544, 6930, 13860, 13860, 3465, 27720, 27720, 637560, 1275120, 182160

Offset: 1

Author

N. J. A. Sloane, Jun 28 2002

Keywords

• nonn
• frac

Examples

			1, 2, 5/2, 3, 13/4, 15/4, 47/12, 25/6, 13/3, 55/12, 281/60, 74/15, ...
		

References

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• R. Sitaramachandrarao, On an error term of Landau - II, The Rocky Mountain Journal of Mathematics, Vol. 15, No. 2 (1985), pp. 579-588.
• Eric Weisstein's World of Mathematics, Totient Summatory Function.

Crossrefs

Cf. A000010, A028415 (numerators).

Programs

Maple

map(denom, ListTools:-PartialSums(map(1/numtheory:-phi, [$1..100]))); # Robert Israel, Apr 16 2019

Mathematica

Denominator[Accumulate[Table[1/EulerPhi[k], {k, 1, 50}]]] (* Amiram Eldar, Sep 18 2022 *)

PARI

a(n) = denominator(sum(k=1, n, 1/eulerphi(k))); \\ Michel Marcus, Sep 18 2022