Voozh

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS