A061091 Number of k with 1 <= k <= n relatively prime to phi(k).

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28

Offset

1,2

Comments

Limit_{n->oo} a(n) * log(log(log(n))) / n = 1/exp(gamma).

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 115-119.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

P. Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948) 75-78.

Steven R. Finch, Euler Totient Function Asymptotic Constants [Broken link]

Steven R. Finch, Euler Totient Function Asymptotic Constants [From the Wayback machine]

Paul Pollack, Numbers which are orders only of cyclic groups, arXiv:2007.09734 [math.NT], 2020.

Z. Ruzsa, Erdős and the integers, J. Number Theory 79 (1999) 115-163.

Formula

a(n) = Sum_{k=1..n} gcd(k, phi(k)) = 1.

a(1) = 1; a(n) = a(n-1) + A297086(n). - Iain Fox, Dec 25 2017

Prog

(PARI) a(n) = sum(k=1, n, gcd(k, eulerphi(k)) == 1) \\ Charles R Greathouse IV, Jan 29 2013 (corrected by Iain Fox, Dec 25 2017)

Crossrefs

Gamma function: A001620, phi function: A000010.

Sequence in context: A185195 A192512 A036234 * A350254 A196241 A086592

Adjacent sequences: A061088 A061089 A061090 * A061092 A061093 A061094

Keyword

nonn,easy

Author

Frank Ellermann, May 29 2001

Status

approved