A250405 Numbers k such that all values of Euler phi (A000010) of all divisors of k are pairwise distinct and represent all proper divisors of k+1.

1, 3, 15, 255, 65535, 4294967295

Offset

1,2

Comments

Numbers k such that {phi(d) : d|k} = {d : d|(k+1), d<(k+1)} as multisets.

Conjecture: last term is 4294967295.

First six terms coincide with A051179. - Omar E. Pol, Apr 12 2025

Links

Table of n, a(n) for n=1..6.

Example

15 is in the sequence because {phi(d) : d|15} = {1, 2, 4, 8} = {d : d|16, d<16}.
2 is not in the sequence because {phi(d) : d|2} = {1, 1}, but {d : d|2, d<2} = {1}.

Prog

(Magma) [n: n in [1..100000] | ([EulerPhi(d): d in Divisors(n)]) eq ([d: d in Divisors(n+1) | d lt n+1 ])];

Crossrefs

Subsequence of A250404 and A203966.

Sequence differs from A051179, A050474 and A116518.

Cf. A000010.

Sequence in context: A247174 A277626 A050474 * A051179 A374341 A374342

Adjacent sequences: A250402 A250403 A250404 * A250406 A250407 A250408

Keyword

nonn,more,hard

Author

Jaroslav Krizek, Nov 22 2014

Extensions

Edited and a(6) added by Max Alekseyev, May 04 2024

Status

approved