cp's OEIS Frontend

Numbers k such that k = A000005(k) * A000010(k-1) + 1.

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

The next term, if it exists, must be greater than 2*10^7.

A prime p is in the sequence iff p is a Fermat prime (A019434) - see proof in A171271.

Observation: the known composite terms are squares of primes. - Omar E. Pol, Nov 04 2015

From Charlie Neder, Mar 02 2019: (Start)

Rearranging the definition gives (k-1)/phi(k-1) = tau(k), which means k-1 is in A007694. Since k-1 is thus 3-smooth, there are two possibilities:

1) k-1 is a power of 2 and tau(k) = 2, i.e., k is a Fermat prime,

2) k-1 is a 3-smooth number divisible by 6 and tau(k) = 3, i.e., k is a Pierpont number and the square of a prime.

In the second case, k-1 factors as (p-1)(p+1) for some p, and both parts are 3-smooth if and only if p is in {2,3,5,7,17} (2 and 3 are excluded since in those cases k-1 is not divisible by 6). Therefore, this sequence is complete if and only if there are no more Fermat primes. (End)