A378637 Largest m <= n such that phi(m) divides n, where phi is the Euler totient function (A000010).

1, 2, 2, 4, 2, 6, 2, 8, 2, 6, 2, 12, 2, 6, 2, 16, 2, 18, 2, 12, 2, 6, 2, 24, 2, 6, 2, 12, 2, 22, 2, 32, 2, 6, 2, 36, 2, 6, 2, 33, 2, 18, 2, 23, 2, 6, 2, 48, 2, 22, 2, 12, 2, 54, 2, 30, 2, 6, 2, 50, 2, 6, 2, 64, 2, 46, 2, 12, 2, 22, 2, 72, 2, 6, 2, 12, 2, 18, 2, 75

Offset: 1

Author

Paolo Xausa, Dec 03 2024

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Right border of A378636.

Cf. A000010, A319048, A378641.

Programs

Mathematica

A378637[n_] := If[OddQ[n] && n > 2, 2, Module[{m = n}, While[!Divisible[n, EulerPhi[m]], m--]; m]];
Array[A378637, 100]

PARI

a(n) = my(m=n); while (n % eulerphi(m), m--); m; \\ Michel Marcus, Dec 05 2024

Formula

a(2*k+1) = 2, for k >= 1.