A384632 a(0)=0. For each digit d in the sequence, let a(n) equal the smallest unused integer which has at least d divisors.

0, 1, 2, 3, 4, 6, 12, 5, 7, 16, 24, 8, 18, 9, 10, 30, 11, 36, 48, 13, 14, 15, 17, 19, 20, 21, 28, 22, 40, 23, 25, 26, 27, 29, 32, 31, 42, 33, 60, 34, 35, 37, 38, 39, 54, 41, 43, 44, 45, 46, 49, 47, 50, 51, 52, 53, 56, 55, 72, 57, 58, 62, 59, 63, 61, 64, 65

Offset: 0

Author

Gavin Lupo, Jun 05 2025

Keywords

• nonn
• base

Examples

			a(0) = 0.
a(1) = Smallest unused integer with at least 0 divisors = 1.
a(2) = Smallest unused integer with at least 1 divisor = 2.
a(3) = Smallest unused integer with at least 2 divisors = 3.
a(4) = Smallest unused integer with at least 3 divisors = 4.
a(5) = Smallest unused integer with at least 4 divisors = 6.
a(6) = Smallest unused integer with at least 6 divisors = 12.
a(7) = Smallest unused integer with at least 1 divisor = 5.
a(8) = Smallest unused integer with at least 2 divisors = 7.
		

Crossrefs

Cf. A000005, A362371, A362551.

Programs

Python

from sympy import divisor_count
a = [0]
for n in range(100):
    if a[n] >= 10:
        split = [int(d) for d in str(a[n])]
    else:
        split = [a[n]]
    for s in split:
        num = 1
        while True:
            if divisor_count(num) >= s and num not in a:
                a.append(num)
                break
            num += 1
print(a)