This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069823 #32 May 27 2024 07:18:41
%S A069823 1,15,25,35,51,65,69,81,85,87,121,123,129,141,143,159,161,177,185,187,
%T A069823 203,213,235,247,249,253,255,265,267,275,289,299,301,309,321,323,339,
%U A069823 341,343,361,393,403,415,425,447,485,489,501,519,527,529,535,537,551
%N A069823 Nonprime numbers k for which there is no x < k such that phi(x) = phi(k).
%C A069823 If p is prime there is no x < p such that phi(x) = phi(p) = p-1 since phi(x) < p-1.
%C A069823 Nonprime numbers k such that A081373(k)=1; i.e., the number of numbers not exceeding k, and with identical phi value to that of k, equals one. - _Labos Elemer_, Mar 24 2003
%C A069823 For 1 < n, if a(n) is squarefree, then phi(a(n)) is nonsquarefree. The converse is also true: for 1 < n, if phi(a(n)) is squarefree then a(n) is nonsquarefree. - _Torlach Rush_, Dec 26 2017
%H A069823 Amiram Eldar, <a href="/A069823/b069823.txt">Table of n, a(n) for n = 1..10000</a>
%e A069823 k=25, a nonprime; phi values for k <= 25 are {1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8,12,10,22,8,20}; no phi(k) except phi(25) equals 20, A081373(25)=1, so 25 is a term.
%t A069823 f[x_] := EulerPhi[x] fc[x_] := Count[Table[f[j]-f[x], {j, 1, x}], 0] t1=Flatten[Position[Table[fc[w], {w, 1, 1000}], 1]] t2=Flatten[Position[PrimeQ[t1], False]] Part[t1, t2]
%t A069823 (* Second program: *)
%t A069823 Union@ Select[Values[PositionIndex@ Array[EulerPhi, 600]][[All, 1]], ! PrimeQ@ # &] (* _Michael De Vlieger_, Dec 31 2017 *)
%o A069823 (PARI) for(s=1,600,if((1-isprime(s))*abs(prod(i=1,s-1,eulerphi(i)-eulerphi(s)))>0, print1(s,",")))
%Y A069823 Cf. A081373, A067004, A000010.
%K A069823 easy,nonn
%O A069823 1,2
%A A069823 _Benoit Cloitre_, Apr 28 2002