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

1, 2, 3, 15, 255, 65535

Offset

1,2

Comments

Numbers n such that {distinct values of phi(d); d|n} == {d; d|(n+1), d<(n+1)}.

Conjecture: next and last term is 4294967295.

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

Links

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

Example

2 is in the sequence because {distinct values of phi(d); d|2} == {1} == {d; d|2, d<2}.
15 is in the sequence because {distinct values of phi(d); d|15} == {1, 2, 4, 8} == {d; d|16, d<16}.

Prog

(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

Crossrefs

Cf. A000010, A203966, A250405.

Sequence in context: A162108 A162100 A330871 * A203966 A167444 A292709

Adjacent sequences: A250401 A250402 A250403 * A250405 A250406 A250407

Keyword

nonn,more

Author

Jaroslav Krizek, Nov 22 2014

Status

approved