Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #57 Jul 31 2024 13:42:55
%S 1,32,3044,304192,30397486,3039650754,303963552392,30396356427242,
%T 3039635516365908,303963551173008414,30396355092886216366,
%U 3039635509283386211140,303963550927059804025910,30396355092702898919527444,3039635509270144893910357854,303963550927013509478708835152
%N a(n) = A002088(10^n) = Sum_{k <= 10^n} phi(k), sum of the Euler totients phi = A000010.
%C 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]
%H Hiroaki Yamanouchi, <a href="/A064018/b064018.txt">Table of n, a(n) for n = 0..18</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientSummatoryFunction.html">Totient Summatory Function.</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Totient_summatory_function">Totient summatory function</a>
%t s = 0; k = 1; Do[ While[ k <= 10^n, s = s + EulerPhi[ k ]; k++ ]; Print[ s ], {n, 0, 8} ]
%Y Cf. A000010, A002088, A104141.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Sep 07 2001
%E More terms from _Robert G. Wilson v_, Sep 07 2001
%E a(10)-a(11) from _Donovan Johnson_, Feb 06 2010
%E a(12) from _Donovan Johnson_, Feb 07 2012
%E a(13)-a(14) from _Hiroaki Yamanouchi_, Jul 06 2014
%E a(15) from _Asif Ahmed_, Apr 16 2015
%E Name edited by _Michel Marcus_ and _M. F. Hasler_, Apr 16 and Apr 18 2015