A108144 Numbers n such that (n-1)/P(n-1) is a power of two > 1, where P(n) is the largest prime factor of n.

5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29, 33, 35, 39, 41, 45, 47, 49, 53, 57, 59, 63, 65, 69, 75, 77, 81, 83, 87, 89, 93, 95, 97, 105, 107, 113, 117, 119, 123, 125, 129, 135, 137, 143, 147, 149, 153, 159, 161, 165, 167, 173, 177, 179, 185, 189, 193, 195, 203, 207

Offset

1,1

Comments

Conjecture: There are infinitely many primes and semiprimes in this sequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

1537 is a term because 1536/3 = 512 = 2^9.

Mathematica

p2Q[n_]:=Module[{c=(n-1)/FactorInteger[n-1][[-1, 1]]}, IntegerQ[Log2[c]] && c>1]; Select[Range[2, 250], p2Q] (* Harvey P. Dale, Aug 17 2020 *)

Crossrefs

Cf. A052126.

Sequence in context: A062545 A020735 A329391 * A241835 A279914 A123910

Adjacent sequences: A108141 A108142 A108143 * A108145 A108146 A108147

Keyword

easy,nonn

Author

Jason Earls, Jul 23 2005

Status

approved