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

Author

Jaroslav Krizek, Nov 22 2014

Keywords

• nonn
• more
• hard

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

Examples

			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}.
		

Crossrefs

Subsequence of A250404 and A203966.

Sequence differs from A051179, A050474 and A116518.

Cf. A000010.

Programs

Magma

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

Extensions

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