A187565 -id:A187565 - cp's OEIS frontend

A187516 Numbers divisible by at least two of their digits, different and >1.

24, 36, 48, 124, 126, 128, 132, 135, 162, 168, 175, 184, 204, 208, 216, 224, 234, 240, 244, 246, 248, 250, 264, 273, 276, 280, 284, 288, 306, 312, 315, 324, 328, 336, 342, 345, 348, 357, 360, 366, 369, 372, 375, 378, 384, 396, 408, 412, 420, 424, 426, 428, 432, 435, 448, 452, 456, 462, 468, 472, 476, 480, 488, 492, 495, 520, 524, 528, 540, 564, 584, 612, 624, 630, 636, 639, 642, 648

Offset: 1

Zak Seidov, Mar 10 2011

There are 225 such integers < 2000, 1679 less than 10^4, 21389 less than 10^5, and 251613 less than 10^6.

Asymptotic density 17/35 = 0.485.... - Charles R Greathouse IV, Mar 11 2011

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A185186, A187238, A187398, A187533, A187534, A187551, A187565, A187584.

s={};Do[un=Select[Union[IntegerDigits[n]],#>1&];cnt=0;Do[d=un[[k]];If[Mod[n,d]==0,cnt++;If[cnt>1,AppendTo[s,n];Goto[ne]]],{k,Length@un}];Label[ne],{n,10000}];s
dtdQ[n_]:=Total[Boole[Divisible[n,Union[Select[IntegerDigits[n], #>1&]]]]]>1; Select[Range[700],dtdQ]

is(n)=my(d=Set(digits(n))); sum(i=1,#d, d[i]>1 && n%d[i]==0)>1 \\ Charles R Greathouse IV, Feb 11 2017

A187238 Numbers divisible by at least four of their digits, different and >1.

Original entry on oeis.org

2364, 2436, 3264, 3276, 3492, 3624, 3648, 3864, 3924, 4236, 4368, 4392, 4632, 4872, 4896, 4932, 4968, 6324, 6384, 6432, 6984, 8496, 8736, 9324, 9432, 9648, 9864, 12384, 12648, 12768, 12864, 13248, 13824, 13896, 13968, 14328, 14728, 14832, 16248, 16824, 17248, 18264

Offset: 1

Zak Seidov, Mar 11 2011

There are 14594 terms < 10^6.

Asymptotic density 10/63 = 0.158.... - Charles R Greathouse IV, Mar 11 2011

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A187398.

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

numdig = 4; Select[Range[23640], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)

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

Original entry on oeis.org

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

Offset: 1

Zak Seidov, Mar 11 2011

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).

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

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 *)

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

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

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A187516 Numbers divisible by at least two of their digits, different and >1.

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A187238 Numbers divisible by at least four of their digits, different and >1.

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

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