A061286 Smallest integer for which the number of divisors is the n-th prime.

2, 4, 16, 64, 1024, 4096, 65536, 262144, 4194304, 268435456, 1073741824, 68719476736, 1099511627776, 4398046511104, 70368744177664, 4503599627370496, 288230376151711744, 1152921504606846976

Offset: 1

Author

Labos Elemer, May 22 2001

Keywords

• nonn
• easy

Comments

Seems to be the same as "Even numbers with prime number of divisors" - Jason Earls, Jul 04 2001

Except for the first term, smallest number == 1 (mod prime(n)) having n divisors (by Fermat's little theorem). - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 20 2003

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..460
• Index to divisibility sequences

Crossrefs

Cf. A000005, A005179, A003680, A061283, A061286, A006093, A005097, A006254, A119523, A196202.

Programs

Mathematica

Table[2^(p-1),{p,Table[Prime[n],{n,1,18}]}] (* Geoffrey Critzer, May 26 2013 *)

PARI

forstep(n=2,100000000,2,x=numdiv(n); if(isprime(x),print(n)))

PARI

a(n)=2^(prime(n)-1) \\ Charles R Greathouse IV, Apr 08 2012

Python

from sympy import isprime, divisor_count as tau
[2] + [2**(2*n) for n in range(1, 33) if isprime(tau(2**(2*n)))] # Karl V. Keller, Jr., Jul 10 2020

Formula

a(n) = 2^(prime(n)-1) = 2^A006093(n).

a(n) = A005179(prime(n)). - R. J. Mathar, Aug 09 2019

Sum_{n>=1} 1/a(n) = A119523. - Amiram Eldar, Aug 11 2020