A249541 Numbers m such that phi(m-2) divides m-1 where phi is Euler's totient function (A000010).

3, 4, 5, 17, 257, 65537, 83623937, 4294967297, 6992962672132097

Offset: 1

Author

Jaroslav Krizek, Feb 25 2015

Keywords

• nonn
• more

Comments

The first 5 known Fermat primes from A019434 are in this sequence.

Corresponding values of numbers k(m) = (m-1) / phi(m-2): 2, 3, 2, 2, 2, 2, 2, 2, ...

Conjecture: 4 is the only number m such that 3*phi(m-2) = m-1. (See comment in A203966.)

Examples

			4 is in the sequence because phi(4-2) = 1 divides 4-1 = 3.
		

Crossrefs

Supersequence of A232720 and A254576.

Cf. A000010, A019434, A203966, A232720, A254576.

Programs

Magma

[n: n in [3..10000000] | (n-1) mod EulerPhi(n-2) eq 0];

Formula

a(n) = A203966(n+1) + 2. - Max Alekseyev, Feb 01 2024

Extensions

a(9) confirmed by Max Alekseyev, Feb 01 2024