A345390 Numbers whose set of divisors contains every digit at least twice.

540, 720, 760, 810, 918, 1080, 1140, 1170, 1260, 1404, 1440, 1512, 1520, 1530, 1560, 1620, 1740, 1800, 1820, 1824, 1836, 1872, 1890, 1908, 1960, 2016, 2028, 2052, 2070, 2072, 2088, 2106, 2112, 2124, 2142, 2156, 2160, 2184, 2208, 2280, 2340, 2380, 2430, 2508, 2520

Offset: 1

Author

Tanya Khovanova, Jun 17 2021

Keywords

• nonn
• base

Comments

Compare to A095050: Numbers such that all ten digits are needed to write all positive divisors in decimal representation.

Examples

			The divisors of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, and 918. Every digit appears at least twice. Thus, 918 is in this sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A059436, A095050.

Programs

Maple

q:= n-> (p-> is(min(seq(coeff(p, x, j), j=0..9))>1))(add(x^i, i=
     map(d-> convert(d, base, 10)[], [numtheory[divisors](n)[]]))):
select(q, [$10..2600])[];  # Alois P. Heinz, Apr 21 2022

Mathematica

Select[Range[3000], Length[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] == 10 && Min[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] > 1 &]

Python

from sympy import divisors
def ok(n):
    digits_used = {d:0 for d in "0123456789"}
    for div in divisors(n, generator=True):
        for d in str(div): digits_used[d] += 1
        if all(digits_used[d] > 1 for d in "0123456789"): return True
    return False
print([k for k in range(2521) if ok(k)]) # Michael S. Branicky, Jun 25 2022