A165318 Primes p where the number of divisors of p-1 is a power of 2.

2, 3, 7, 11, 23, 31, 41, 43, 47, 59, 67, 71, 79, 83, 89, 103, 107, 131, 137, 139, 167, 179, 191, 211, 223, 227, 233, 239, 251, 263, 271, 281, 283, 311, 313, 331, 347, 359, 367, 379, 383, 409, 419, 431, 439, 443, 457, 463, 467, 479, 499, 503, 521, 547, 563, 569

Offset: 1

Author

Leroy Quet, Sep 14 2009

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000005, A008328, A036537, A165319, A165320.

Programs

Maple

isA000079 := proc(n) RETURN( n=1 or numtheory[factorset](n) = {2}) ; end: A165318 := proc(n) if n = 1 then 2; else p := nextprime(procname(n-1)) ; while not isA000079(numtheory[tau](p-1)) do p := nextprime(p) ; od; p ; fi; end: seq(A165318(n),n=1..90) ; # R. J. Mathar, Sep 18 2009

Mathematica

Select[Prime[Range[200]],IntegerQ[Log[2,DivisorSigma[0,#-1]]]&] (* Harvey P. Dale, Oct 14 2018 *)

PARI

isok(p) = isprime(p) && apply(x -> x >> valuation(x, 2), numdiv(p-1)) == 1; \\ Amiram Eldar, Jun 26 2025

Extensions

More terms from R. J. Mathar, Sep 18 2009