A345390 - OEIS

%I #19 Jul 11 2022 08:38:15

%S 540,720,760,810,918,1080,1140,1170,1260,1404,1440,1512,1520,1530,

%T 1560,1620,1740,1800,1820,1824,1836,1872,1890,1908,1960,2016,2028,

%U 2052,2070,2072,2088,2106,2112,2124,2142,2156,2160,2184,2208,2280,2340,2380,2430,2508,2520

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

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

%H Michael S. Branicky, <a href="/A345390/b345390.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 q:= n-> (p-> is(min(seq(coeff(p, x, j), j=0..9))>1))(add(x^i, i=

%p      map(d-> convert(d, base, 10)[], [numtheory[divisors](n)[]]))):

%p select(q, [$10..2600])[];  # _Alois P. Heinz_, Apr 21 2022

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

%o (Python)

%o from sympy import divisors

%o def ok(n):

%o     digits_used = {d:0 for d in "0123456789"}

%o     for div in divisors(n, generator=True):

%o         for d in str(div): digits_used[d] += 1

%o         if all(digits_used[d] > 1 for d in "0123456789"): return True

%o     return False

%o print([k for k in range(2521) if ok(k)]) # _Michael S. Branicky_, Jun 25 2022

%Y Cf. A059436, A095050.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Jun 17 2021