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

1,1

Comments

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

Links

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

Example

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.

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 &]

Prog

(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

Crossrefs

Cf. A059436, A095050.

Sequence in context: A184546 A252386 A289221 * A261290 A253463 A255105

Adjacent sequences: A345387 A345388 A345389 * A345391 A345392 A345393

Keyword

nonn,base

Author

Tanya Khovanova, Jun 17 2021

Status

approved