OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Olivier Bordellès, Randell Heyman, Igor E. Shparlinski, On a sum involving the Euler function, arXiv:1808.00188 [math.NT], 2018.
FORMULA
a(n) <= (1/2)*(1 + 1/zeta(2))*n*log(n) + 4*n + sqrt(n)*log(n)/4 + sqrt(n), uniformly for n >= 3.
a(n) >= ((2629/4009)+o(1))*n*log(n)/zeta(2) as n approaches infinity.
Cautious conjecture: a(n) ~ n*log(n)/zeta(2).
EXAMPLE
a(4) = phi(floor(4/1)+phi(floor(4/2))+phi(floor(4/3))+phi(floor(4/4)) = phi(4)+phi(2)+phi(1)+phi(1) = 2+1+1+1 = 5.
MAPLE
with(numtheory): S:=0: for x to 30 do: for m to x do: S := S+phi(trunc(x/m)) end do; print(x, S); S := 0:end do:
MATHEMATICA
Array[Sum[EulerPhi[Floor[#/k]], {k, #}] &, 65] (* Michael De Vlieger, Aug 02 2018 *)
PROG
(PARI) a(n) = sum(x=1, n, eulerphi(n\x)); \\ Michel Marcus, Aug 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Randell G Heyman, Aug 02 2018
EXTENSIONS
More terms from Michel Marcus, Aug 02 2018
STATUS
approved