A283107 Numbers k such that tau(4*(k - 1)) is prime.

2, 5, 17, 257, 1025, 16385, 65537, 1048577, 67108865, 268435457, 17179869185, 274877906945, 1099511627777, 17592186044417, 1125899906842625, 72057594037927937, 288230376151711745

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 28 2017

Keywords

• nonn

Comments

Conjecturally, a supersequence of A281312.

The conjecture is true: the formula at A281312 implies that the number of divisors of 4*A281312(n) - 4 is A000043(n+1). - Charles R Greathouse IV, Mar 01 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..467

Crossrefs

Supersequence of A281312.

Cf. A000005, A258429.

Programs

Magma

[n: n in [2..1100000] | IsPrime(NumberOfDivisors(4*(n-1)))];

Mathematica

Select[Range[2, 10^7], PrimeQ@ DivisorSigma[0, 4 (# - 1)] &] (* Michael De Vlieger, Feb 28 2017 *)

PARI

is(n)=isprime(numdiv(4*n-4)) \\ Charles R Greathouse IV, Feb 28 2017

PARI

list(lim)=my(v=List()); forprime(p=3,logint(lim\1*8-8,2), listput(v,2^(p-3)+1)); Vec(v) \\ Charles R Greathouse IV, Mar 01 2017

Extensions

a(4), a(9)-a(17) from Charles R Greathouse IV, Mar 01 2017