A174322 a(n) is the smallest n-digit number with exactly 4 divisors.

6, 10, 106, 1003, 10001, 100001, 1000001, 10000001, 100000001, 1000000006, 10000000003, 100000000007, 1000000000007, 10000000000015, 100000000000013, 1000000000000003, 10000000000000003, 100000000000000015, 1000000000000000007, 10000000000000000001

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• base

Comments

a(n) = the smallest n-digit number of the form p^3 or p^1*q^1, (p, q = distinct primes).

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..70

Crossrefs

Subsequence of A030513.

Cf. A182648 (largest n-digit numbers with exactly 4 divisors).

Programs

Mathematica

Table[k=10^(n-1); While[DivisorSigma[0, k] != 4, k++]; k, {n, 10}]

Python

from sympy import divisors
def a(n):
    k = 10**(n-1)
    while len(divisors(k)) != 4: k += 1
    return k
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jun 10 2021

Python

# faster alternative for larger terms
from sympy import divisors
def a(n):
    k = 10**(n-1) - 1
    divs = -1
    while divs != 4:
      k += 1
      divs = 0
      for d in divisors(k, generator=True):
        divs += 1
        if divs > 4: break
    return k
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Jun 10 2021

Formula

A000005(a(n)) = 4.