cp's OEIS Frontend

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

%I A061070 #13 Sep 10 2023 00:42:39
%S A061070 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,
%T A061070 13,13,13,13,14,14,15,15,15,15,16,16,17,17,17,17,18,18,18,18,19,19,20,
%U A061070 20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,25,25,26,26,27,27,27,27
%N A061070 Number of distinct values in the list of values of the Euler totient function {phi(j) : j=1..n}.
%H A061070 T. D. Noe, <a href="/A061070/b061070.txt">Table of n, a(n) for n=1..1000</a>
%H A061070 Terence Tao, <a href="https://arxiv.org/abs/2309.02325">Monotone non-decreasing sequences of the Euler totient function</a>, arXiv:2309.02325 [math.NT], 2023.
%F A061070 a(n) = | {phi(j) : j=1..n} |.
%e A061070 From _Michael De Vlieger_, Sep 09 2023: (Start)
%e A061070 a(1) = 1 since phi(1) = 1 is distinct from phi(k), k < 1.
%e A061070 a(2) = 1 since phi(2) = phi(1).
%e A061070 a(3) = 2 since phi(3) = 2, distinct from phi(1) = phi(2) = 1.
%e A061070 a(4) = 2 since phi(4) = phi(3) = 2.
%e A061070 a(5) = 3 since phi(5) = 4, distinct from phi(k), k < 5, etc. (End)
%t A061070 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 *)
%o A061070 (Python)
%o A061070 from sympy import totient
%o A061070 def A061070(n): return len({totient(i) for i in range(1,n+1)}) # _Chai Wah Wu_, Sep 08 2023
%Y A061070 Cf. A000010.
%K A061070 nonn
%O A061070 1,3
%A A061070 _Labos Elemer_, May 28 2001