A250405 Numbers n such that the multiset of all values of phi of all divisors of n equals the multiset of all proper divisors of n+1 where phi is the Euler totient function (A000010).

1, 3, 15, 255, 65535

Offset

1,2

Comments

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

Conjecture: next and last term is 4294967295.

Sequence differs from A051179, A050474 and A116518.

Links

Table of n, a(n) for n=1..5.

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

Cf. A000010, A250404.

Sequence in context: A257018 A173146 A139289 * A116518 A247174 A277626

Adjacent sequences: A250402 A250403 A250404 * A250406 A250407 A250408

Keyword

nonn

Author

Jaroslav Krizek, Nov 22 2014

Status

approved