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

%I A345390 #19 Jul 11 2022 08:38:15
%S A345390 540,720,760,810,918,1080,1140,1170,1260,1404,1440,1512,1520,1530,
%T A345390 1560,1620,1740,1800,1820,1824,1836,1872,1890,1908,1960,2016,2028,
%U A345390 2052,2070,2072,2088,2106,2112,2124,2142,2156,2160,2184,2208,2280,2340,2380,2430,2508,2520
%N A345390 Numbers whose set of divisors contains every digit at least twice.
%C A345390 Compare to A095050: Numbers such that all ten digits are needed to write all positive divisors in decimal representation.
%H A345390 Michael S. Branicky, <a href="/A345390/b345390.txt">Table of n, a(n) for n = 1..10000</a>
%e A345390 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.
%p A345390 q:= n-> (p-> is(min(seq(coeff(p, x, j), j=0..9))>1))(add(x^i, i=
%p A345390      map(d-> convert(d, base, 10)[], [numtheory[divisors](n)[]]))):
%p A345390 select(q, [$10..2600])[];  # _Alois P. Heinz_, Apr 21 2022
%t A345390 Select[Range[3000], Length[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] == 10 && Min[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] > 1 &]
%o A345390 (Python)
%o A345390 from sympy import divisors
%o A345390 def ok(n):
%o A345390     digits_used = {d:0 for d in "0123456789"}
%o A345390     for div in divisors(n, generator=True):
%o A345390         for d in str(div): digits_used[d] += 1
%o A345390         if all(digits_used[d] > 1 for d in "0123456789"): return True
%o A345390     return False
%o A345390 print([k for k in range(2521) if ok(k)]) # _Michael S. Branicky_, Jun 25 2022
%Y A345390 Cf. A059436, A095050.
%K A345390 nonn,base
%O A345390 1,1
%A A345390 _Tanya Khovanova_, Jun 17 2021