OFFSET
0,2
COMMENTS
Asymptotically, A002088(n) ~ 0.30396355...*n^2 = (3/Pi^2)*n^2, see A104141 and A002088. - Michael B. Porter, Mar 08 2013 [corrected by M. F. Hasler, Apr 18 2015]
LINKS
Lucas A. Brown, Table of n, a(n) for n = 0..19 (terms 0..18 from Hiroaki Yamanouchi)
Lucas A. Brown, Python program.
Lucas Augustus Brown, Computation of the Totient Summatory Function, arXiv:2506.07386 [math.NT], 2025.
Eric Weisstein's World of Mathematics, Totient Summatory Function.
Wikipedia, Totient summatory function.
FORMULA
a(n) = Sum_{k <= 10^n} A000010(k).
EXAMPLE
a(1) = phi(1) + ... + phi(10) = 1 + 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 + 4 = 32.
MATHEMATICA
s = 0; k = 1; Do[ While[ k <= 10^n, s = s + EulerPhi[ k ]; k++ ]; Print[ s ], {n, 0, 8} ]
PROG
(Python) # See LINKS. - Lucas A. Brown, Jun 08 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 07 2001
EXTENSIONS
More terms from Robert G. Wilson v, Sep 07 2001
a(10)-a(11) from Donovan Johnson, Feb 06 2010
a(12) from Donovan Johnson, Feb 07 2012
a(13)-a(14) from Hiroaki Yamanouchi, Jul 06 2014
a(15) from Asif Ahmed, Apr 16 2015
Name edited by Michel Marcus and M. F. Hasler, Apr 16 and Apr 18 2015
STATUS
approved