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A061091 Number of k with 1 <= k <= n relatively prime to phi(k). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)