A187584 Least number divisible by at least n of its digits, different and > 1.

2, 24, 248, 2364, 27384, 243768, 23469768, 1234759680

Offset: 1

Author

Zak Seidov, Mar 11 2011

Keywords

• nonn
• base
• fini
• full

Comments

a(1)=2=A185186(1), a(2)=24=A187516(1),

a(3)=248=A187398(1), a(4)=2364=A187238(1),

a(5)=27384=A187533(1), a(6)=243768=A187534(1),

a(7)=23469768=A187551(1), a(8)=1234759680=A187565(1).

Crossrefs

Cf. A185186, A187238, A187398, A187516, A187533, A187534, A187551, A187565.

Programs

Mathematica

divQ[m_, n_] := Length[(u = Union[Select[IntegerDigits[m], # > 1 &]])] >= n && Plus @@ (Boole@Divisible[m, u]) >= n; a[n_] := Module[{k = 1}, While[! divQ[k, n], k++]; k]; Array[a, 8] (* Amiram Eldar, Aug 30 2020 *)

Python

def c(n): return len(set(d for d in str(n) if d>'1' and n%int(d)==0))
def a(n):
  m = 2*10**(n-1)
  while c(m) < n: m += 1
  return m
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Feb 24 2021

Extensions

a(8) corrected by David A. Corneth, Aug 30 2020