A283107 - OEIS

%I #20 Nov 21 2024 21:25:57

%S 2,5,17,257,1025,16385,65537,1048577,67108865,268435457,17179869185,

%T 274877906945,1099511627777,17592186044417,1125899906842625,

%U 72057594037927937,288230376151711745

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

%C Conjecturally, a supersequence of A281312.

%C 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

%H Charles R Greathouse IV, <a href="/A283107/b283107.txt">Table of n, a(n) for n = 1..467</a>

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

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

%o (PARI) is(n)=isprime(numdiv(4*n-4)) \\ _Charles R Greathouse IV_, Feb 28 2017

%o (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

%Y Supersequence of A281312.

%Y Cf. A000005, A258429.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 28 2017

%E a(4), a(9)-a(17) from _Charles R Greathouse IV_, Mar 01 2017