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

1,1

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

Table of n, a(n) for n=1..9.

Henri Lifchitz and Renaud Lifchitz, Phi(258121,2)/719.

Wikipedia, Unique prime, section Binary unique primes.

Prog

(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, ", "))

Crossrefs

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

Sequence in context: A265946 A027888 A332925 * A027887 A088383 A067496

Adjacent sequences: A333970 A333971 A333972 * A333974 A333975 A333976

Keyword

nonn,hard,more

Author

Jeppe Stig Nielsen, Sep 22 2020

Status

approved