A182648 a(n) is the largest n-digit number with exactly 4 divisors.

8, 95, 998, 9998, 99998, 999997, 9999998, 99999997, 999999991, 9999999997, 99999999997, 999999999997, 9999999999989, 99999999999997, 999999999999998, 9999999999999994, 99999999999999989, 999999999999999993, 9999999999999999991, 99999999999999999983

Offset

1,1

Comments

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

Large overlap with A098450 which considers p^2 and p*q with n digits. - R. J. Mathar, Apr 23 2024

Links

Michael S. Branicky, Table of n, a(n) for n = 1..62

Formula

A000005(a(n)) = 4.

Mathematica

Table[k=10^n-1; While[DivisorSigma[0, k] != 4, k--]; k, {n, 10}]
lnd4[n_]:=Module[{k=10^n-1}, While[DivisorSigma[0, k]!=4, k--]; k]; Array[lnd4, 20] (* Harvey P. Dale, Aug 20 2024 *)

Prog

(Python)
from sympy import divisors
def a(n):
    k = 10**n - 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, 21)]) # Michael S. Branicky, Jun 10 2021

Crossrefs

Subsequence of A030513.

Cf. A174322, A098450.

Sequence in context: A298659 A299611 A099298 * A003775 A262737 A299747

Adjacent sequences: A182645 A182646 A182647 * A182649 A182650 A182651

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Extensions

a(19) and beyond from Michael S. Branicky, Jun 10 2021

Status

approved