A221283 Number of totients up to 10^n.

1, 6, 38, 291, 2374, 20254, 180184, 1634372, 15037909, 139847905, 1311179363, 12372781988

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Kevin Ford, The distribution of totients, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), pp. 27-34.

Kevin Ford, The distribution of totients, The Ramanujan Journal, Vol. 2 (1998), pp. 67-151; arXiv preprint, arXiv:1104.3264 [math.NT], 2011-2013.

Formula

a(n) is about 10^n/n * 2.2655434...^((log log n)^2); see Theorem 1 in the Ford paper for a more precise asymptotic.

Example

There are 6 totients up to 10: {1 = phi(1), 2 = phi(3), 4 = phi(5), 6 = phi(7), 8 = phi(15), 10 = phi(11)}, so a(1) = 6.

Prog

(PARI) a(n)=sum(k=1, 10^n, istotient(k));

Crossrefs

Cf. A002202, A000010.

Sequence in context: A192941 A263855 A354326 * A064309 A075197 A356458

Adjacent sequences: A221280 A221281 A221282 * A221284 A221285 A221286

Keyword

nonn,hard,more

Author

Charles R Greathouse IV, Feb 06 2013

Extensions

a(10) from Charles R Greathouse IV, Feb 11 2013

a(11) from Amiram Eldar, Jan 29 2025

Status

approved