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A345390 Numbers whose set of divisors contains every digit at least twice. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Compare to A095050: Numbers such that all ten digits are needed to write all positive divisors in decimal representation.
LINKS
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
Sequence in context: A184546 A252386 A289221 * A261290 A253463 A255105
KEYWORD
nonn,base
AUTHOR
Tanya Khovanova, Jun 17 2021
STATUS
approved

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Last modified May 25 14:17 EDT 2024. Contains 372788 sequences. (Running on oeis4.)