A389187 a(n) is the least number ending in at least n identical digits that has exactly n distinct prime divisors.

2, 22, 222, 6666, 111111, 222222, 462222222, 58422222222, 11523666666666, 1141362222222222, 42481455555555555, 1173711888888888888, 579771522222222222222

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Formula

a(n) >= max{A002110(n), A002275(n)}.

a(n) <= A002275(A086565(n)).

Example

2 = 2 has one distinct prime factor;
22 = 2 * 11 has two and 11 only has 1;
222 = 2 * 3 * 37 has three and 111 = 3 * 37 only has 2;
etc.

Prog

(Python)
from sympy import factorint
from itertools import count
def f(n): return len(factorint(n))
def a(n):
    Rn, pow10 = (10**n-1)//9, 10**n
    return next(t for d in count(0) for r in range(10**(d-1) if d else 0, 10**d) for m in range(1, 10) if f(t:=r*pow10 + m*Rn) == n)
print([a(n) for n in range(1, 10)])

Crossrefs

Cf. A001221, A002110, A002275, A086565, A388789.

Sequence in context: A374665 A384403 A388789 * A112893 A086855 A089182

Adjacent sequences: A389184 A389185 A389186 * A389188 A389189 A389190

Keyword

nonn,base,more

Author

Michael S. Branicky, Sep 25 2025

Extensions

a(13) from Daniel Suteu, Oct 22 2025

Status

approved