A064018 a(n) = A002088(10^n) = Sum_{k <= 10^n} phi(k), sum of the Euler totients phi = A000010.

1, 32, 3044, 304192, 30397486, 3039650754, 303963552392, 30396356427242, 3039635516365908, 303963551173008414, 30396355092886216366, 3039635509283386211140, 303963550927059804025910, 30396355092702898919527444, 3039635509270144893910357854, 303963550927013509478708835152

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

Hiroaki Yamanouchi, Table of n, a(n) for n = 0..18

Eric Weisstein's World of Mathematics, Totient Summatory Function.

Wikipedia, Euler's totient function

Mathematica

s = 0; k = 1; Do[ While[ k <= 10^n, s = s + EulerPhi[ k ]; k++ ]; Print[ s ], {n, 0, 8} ]

Crossrefs

Cf. A000010, A002088, A104141.

Sequence in context: A220299 A264115 A113500 * A067321 A104652 A219228

Adjacent sequences: A064015 A064016 A064017 * A064019 A064020 A064021

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