A061070 Number of distinct values in the list of values of the Euler totient function {phi(j) : j=1..n}.

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

Offset: 1

Author

Labos Elemer, May 28 2001

Keywords

• nonn

Examples

			From _Michael De Vlieger_, Sep 09 2023: (Start)
a(1) = 1 since phi(1) = 1 is distinct from phi(k), k < 1.
a(2) = 1 since phi(2) = phi(1).
a(3) = 2 since phi(3) = 2, distinct from phi(1) = phi(2) = 1.
a(4) = 2 since phi(4) = phi(3) = 2.
a(5) = 3 since phi(5) = 4, distinct from phi(k), k < 5, etc. (End)
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Terence Tao, Monotone non-decreasing sequences of the Euler totient function, arXiv:2309.02325 [math.NT], 2023.

Crossrefs

Cf. A000010.

Programs

Mathematica

nn = 120; c[] := False; k = 0; Reap[Do[If[! c[#], k++; c[#] = True] &[EulerPhi[i]]; Sow[k], {i, nn}]][[-1, 1]] (* _Michael De Vlieger, Sep 09 2023 *)

Python

from sympy import totient
def A061070(n): return len({totient(i) for i in range(1,n+1)}) # Chai Wah Wu, Sep 08 2023

Formula

a(n) = | {phi(j) : j=1..n} |.