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

1,1

Comments

Every multiple of a term is also a term.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

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.

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 &]

Prog

(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
(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

Crossrefs

Cf. A059436 (at least n times).

Subsequence of A095050 (at least once) and of A345390 (at least twice).

Sequence in context: A027545 A357496 A113708 * A206112 A232133 A261572

Adjacent sequences: A353063 A353064 A353065 * A353067 A353068 A353069

Keyword

nonn,base

Author

Tanya Khovanova, Apr 21 2022

Status

approved