A333973 Numbers k such that A019320(k) is greater than A064078(k) and the latter is a prime or a prime power.

18, 20, 21, 54, 147, 342, 602, 889, 258121

Offset: 1

Author

Jeppe Stig Nielsen, Sep 22 2020

Keywords

• nonn
• hard
• more

Comments

The unique prime factor of A064078(k) is then a unique prime to base 2 (see A161509), but not a cyclotomic number.

Subsequence of A161508. In fact, subsequence of the set difference A161508 \ A072226.

In all known examples, A064078(k) is a prime. If A064078(k) was a prime power p^j with j>1, then p would be both a Wieferich prime (A001220) and a unique prime to base 2.

Subsequence of A093106 (the characterization of A093106 can be useful when searching for more terms).

Should this sequence be infinite?

Links

• Henri Lifchitz and Renaud Lifchitz, Phi(258121,2)/719.
• Wikipedia, Unique prime, section Binary unique primes.

Crossrefs

Cf. A019320, A064078, A093106, A072226, A144755, A161508, A161509, A247071.

Programs

PARI

for(n=1,+oo,c=polcyclo(n,2); c % n < 2 && next(); c/=(c%n); ispseudoprime(if(ispower(c,,&b),b,c))&&print1(n, ", "))