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

1,1

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

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A338364 A060656 A271234 * A288756 A019279 A061652

Adjacent sequences: A061283 A061284 A061285 * A061287 A061288 A061289

Keyword

nonn,easy

Author

Labos Elemer, May 22 2001

Status

approved