A250404 Numbers k such that the set of all distinct values of phi of all divisors of k equals the set of all proper divisors of k+1 where phi is the Euler totient function (A000010).

1, 2, 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 sets.

Conjecture: last term is 4294967295.

Sequence differs from A203966 because 83623935 is not in this sequence.

Examples

			2 is a term since {phi(d) : d|2} = {1} = {d; d|2, d<2}.
15 is a term since {phi(d) : d|15} = {1, 2, 4, 8} = {d : d|16, d<16}.
		

Crossrefs

Subsequence of A203966.

Cf. A000010, A203966, A250405.

Programs

Magma

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

PARI

isok(n) = {sphi = []; fordiv(n, d, sphi = Set(concat(sphi, eulerphi(d)))); sphi == setminus(Set(divisors(n+1)), Set(n+1));} \\ Michel Marcus, Nov 23 2014

Extensions

Edited and a(7) added by Max Alekseyev, May 04 2024