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A221283 Number of totients up to 10^n. 0
1, 6, 38, 291, 2374, 20254, 180184, 1634372, 15037909, 139847905, 1311179363 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..10.

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

K. Ford, The distribution of totients, Ramanujan J. 2 (1998), pp. 67-151.

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: A082427 A192941 A263855 * A064309 A075197 A276473

Adjacent sequences:  A221280 A221281 A221282 * A221284 A221285 A221286

KEYWORD

nonn,hard

AUTHOR

Charles R Greathouse IV, Feb 06 2013

EXTENSIONS

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

STATUS

approved

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Last modified May 8 12:23 EDT 2021. Contains 343666 sequences. (Running on oeis4.)