A340870 a(n) is the smallest prime p such that p - 1 has 2*n divisors.

3, 7, 13, 31, 113, 61, 193, 211, 181, 241, 13313, 421, 12289, 2113, 1009, 1321, 2424833, 1801, 786433, 2161, 4801, 15361, 155189249, 2521, 6481, 61441, 6301, 8641, 3489660929, 12241, 3221225473, 7561, 64513, 1376257, 58321, 12601, 206158430209, 8650753, 184321

Offset

1,1

Comments

First differs from A080372(n) + 1 for n = 17, where a(17) = 2424833, whereas A080372(17) + 1 = 2162689. - Hugo Pfoertner, Jan 26 2021

Links

Table of n, a(n) for n=1..39.

Formula

tau(a(n) - 1) = 2*n.

Example

a(4) = 31 because 31 is the smallest prime p such that p - 1 has 2*4 divisors; tau(30) = 8.

Mathematica

a={}; For[n=1, n<=40, n++, i=1; While[DivisorSigma[0, Prime[i]-1]!=2n, i++]; AppendTo[a, Prime[i]]]; a (* Stefano Spezia, Jan 25 2021 *)

Prog

(Magma) Ax:=func<n|exists(r){m:m in[2..10^7] | IsPrime(m) and #Divisors(m - 1) eq n*#Divisors(m)}select r else 0>; [Ax(n): n in[1..20]]
(PARI) a(n) = my(p=2); while(numdiv(p-1) != 2*n, p=nextprime(p+1)); p; \\ Michel Marcus, Jan 25 2021

Crossrefs

Cf. A000005 (tau), A080372, A008328.

Cf. A066814 (p-1 has n divisors), A340799 (p+1 has 2*n divisors).

Sequence in context: A176589 A077314 A069246 * A253850 A087578 A023195

Adjacent sequences: A340867 A340868 A340869 * A340871 A340872 A340873

Keyword

nonn

Author

Jaroslav Krizek, Jan 24 2021

Status

approved