A165319 Primes p where the number of divisors of p+1 is a power of 2.

2, 5, 7, 13, 23, 29, 37, 41, 53, 61, 73, 101, 103, 109, 113, 127, 137, 151, 157, 167, 173, 181, 193, 229, 257, 263, 269, 277, 281, 311, 313, 317, 353, 373, 383, 389, 397, 401, 409, 421, 433, 439, 457, 461, 487, 509, 541, 569, 593, 601, 613, 617, 631, 641, 653

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Maple

b:= proc(n) option remember; is(n=2^ilog2(n)) end:
a:= proc(n) option remember; local p; p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if andmap(b, map(i-> i[2]+1, ifactors(p+1)[2])) then break fi
      od; p
    end:
seq(a(n), n=1..55);  # Alois P. Heinz, Sep 05 2019

Mathematica

okQ[p_] := PrimeQ[p] && IntegerQ[Log[2, DivisorSigma[0, p+1]]];
Select[Prime[Range[200]], okQ] (* Jean-François Alcover, May 20 2020 *)

Prog

(PARI) isok(p) = isprime(p) && (nd = numdiv(p+1)) && (nd == 2^valuation(nd, 2)); \\ Michel Marcus, Sep 05 2019

Crossrefs

Cf. A165318, A165320.

Cf. A008329. [R. J. Mathar, Sep 20 2009]

Sequence in context: A261581 A045355 A252281 * A094712 A095281 A106889

Adjacent sequences: A165316 A165317 A165318 * A165320 A165321 A165322

Keyword

nonn

Author

Leroy Quet, Sep 14 2009

Extensions

Extended by R. J. Mathar, Sep 20 2009

Status

approved