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

2, 6, 6, 12, 12, 18, 18, 30, 30, 30, 30, 42, 42, 42, 42, 60, 60, 60, 60, 66, 66, 66, 66, 90, 90, 90, 90, 90, 90, 90, 90, 120, 120, 120, 120, 126, 126, 126, 126, 150, 150, 150, 150, 150, 150, 150, 150, 210, 210, 210, 210, 210, 210, 210, 210

Offset: 1

Author

Jean-François Alcover, Jan 08 2015

Keywords

• nonn

Comments

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

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..1000
• MathOverflow, The maximum of the preimage of [1,x] through Euler's totient function
• Eric Weisstein's World of Mathematics, Totient Function
• Wikipedia, Euler's totient function

Crossrefs

Cf. A000010, A007614, A032447, A036912, A036913, A057635.

Programs

Mathematica

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}]