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A253215 a(n) is the greatest positive integer m such that phi(m) <= n where phi is Euler's totient function.

%I A253215 #27 Feb 16 2025 08:33:24
%S A253215 2,6,6,12,12,18,18,30,30,30,30,42,42,42,42,60,60,60,60,66,66,66,66,90,
%T A253215 90,90,90,90,90,90,90,120,120,120,120,126,126,126,126,150,150,150,150,
%U A253215 150,150,150,150,210,210,210,210,210,210,210,210
%N A253215 a(n) is the greatest positive integer m such that phi(m) <= n where phi is Euler's totient function.
%C A253215 If all duplicates are removed the result is A036913. The indices where a(n) takes a new value are A036912. - _Jeppe Stig Nielsen_, Sep 28 2021
%H A253215 Jean-François Alcover, <a href="/A253215/b253215.txt">Table of n, a(n) for n = 1..1000</a>
%H A253215 MathOverflow, <a href="http://mathoverflow.net/questions/180423">The maximum of the preimage of [1,x] through Euler's totient function</a>
%H A253215 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>
%H A253215 Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler%27s_phi_function">Euler's totient function</a>
%t A253215 inversePhi[m_?EvenQ] := Module[{p, nmax, n, nn}, p = Select[Divisors[m]+1, PrimeQ]; nmax = m*Times @@ (p/(p-1)); n = m; nn = {}; While[n <= nmax, If[EulerPhi[n] == m, AppendTo[nn, n]]; n++]; nn]; a[1] = 2; a[n_?OddQ] := a[n-1]; a[n_] := a[n] = Module[{m}, m = inversePhi[n] // Max; If[m > a[n-1], m, a[n-1]]]; Table[a[n], {n, 1, 100}]
%Y A253215 Cf. A000010, A007614, A032447, A036912, A036913, A057635.
%K A253215 nonn
%O A253215 1,1
%A A253215 _Jean-François Alcover_, Jan 08 2015