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

1,1

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

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}]

Crossrefs

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

Sequence in context: A071892 A064797 A053319 * A075779 A241301 A140880

Adjacent sequences: A253212 A253213 A253214 * A253216 A253217 A253218

Keyword

nonn

Author

Jean-François Alcover, Jan 08 2015

Status

approved