A353066 Numbers whose set of divisors contains every digit at least three times.
1140, 1890, 2280, 2340, 2610, 2660, 2700, 2808, 2880, 2940, 2970, 3420, 3480, 3510, 3540, 3600, 3654, 3672, 3780, 3870, 3920, 3952, 3990, 4032, 4140, 4320, 4368, 4380, 4410, 4560, 4590, 4680, 4740, 4760, 4770, 4860, 4896, 4940, 4950, 5130, 5220, 5320, 5400, 5454
Offset: 1
Examples
The divisors of 1140 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140. Digits tally from 0 to 9: 8, 10, 6, 4, 3, 6, 3, 3, 4, 3. The minimum is 3, thus, 1140 is in this sequence.
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
q:= n-> (p-> is(min(seq(coeff(p, x, j), j=0..9))>2))(add(x^i, i= map(d-> convert(d, base, 10)[], [numtheory[divisors](n)[]]))): select(q, [$10..5555])[]; # Alois P. Heinz, Apr 21 2022 -
Mathematica
Select[Range[10000], Length[Tally[Flatten[IntegerDigits[Divisors[#]]]]] == 10 && Min[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] >= 3 &]
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PARI
upto(n) = { my(v = vector(n, i, -1)); for(i = 1, n, if(v[i] == -1, c = is(i); if(c == 1, v[i] = 1; for(j = 1, n\i, v[i*j] = 1; ) , v[i] = 0 ) ) ); Vec(select(x->x==1,v,1)) } is(n) = { my(v = vector(10, i, 3), d = divisors(n), todo = 30, i, j); for(i = 1, #d, dd = digits(d[i]); for(j = 1, #dd, if(v[dd[j]+1] > 0, v[dd[j]+1]--; todo--; if(todo <= 0, return(1) ) ) ) ); 0 } \\ David A. Corneth, Jul 11 2022 -
Python
from sympy import divisors def ok(n): counts = [0]*10 for d in divisors(n, generator=True): for di in str(d): counts[int(di)] += 1 if min(counts) > 2: return True return False print([k for k in range(5455) if ok(k)]) # Michael S. Branicky, Apr 21 2022
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