A064016 a(n) = Sum_{k <= 10^n} cototient(k), where cototient is A051953.

0, 23, 2006, 196308, 19607514, 1960399246, 196036947608, 19603648572758, 1960364533634092, 196036449326991586, 19603644912113783634, 1960364490766613788860, 196036449073440195974090, 19603644907302101080472556, 1960364490729905106089642146, 196036449072986990521291164848

Offset: 0

Author

Robert G. Wilson v, Sep 07 2001

Keywords

• nonn

Comments

It appears that lim_{n->infinity} (1/n^2) * Sum_{j=1..n} a(j) = 0.1960364... = (1/2 - 3/Pi^2).

Crossrefs

Cf. A002088, A051953, A063985, A064018.

Programs

Mathematica

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

Formula

a(n) = 10^n*(10^n+1)/2 - A002088(10^n) = 10^n*(10^n+1)/2 - A064018(n). - Chai Wah Wu, Apr 18 2021

a(n) = A063985(10^n). - Michel Marcus, Apr 18 2021

Extensions

a(9) from Jud McCranie, Jun 25 2005

a(10)-a(11) from Donovan Johnson, Feb 06 2010

a(12) from Donovan Johnson, Feb 07 2012

a(13)-a(15) using A064018 from Chai Wah Wu, Apr 18 2021