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A333973
Numbers k such that A019320(k) is greater than A064078(k) and the latter is a prime or a prime power.
1
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
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, ", "))
KEYWORD
nonn,hard,more
AUTHOR
Jeppe Stig Nielsen, Sep 22 2020
STATUS
approved