A187516 -id:A187516 - cp's OEIS frontend

A187398 Numbers divisible by at least three of their digits, all different and >1.

248, 264, 324, 384, 396, 432, 624, 648, 672, 728, 735, 784, 824, 864, 936, 1236, 1248, 1296, 1326, 1362, 1368, 1395, 1632, 1692, 1764, 1824, 1926, 1935, 1962, 2048, 2064, 2136, 2184, 2196, 2248, 2304, 2316, 2328, 2340, 2346, 2364, 2376, 2384, 2394, 2408, 2436, 2448, 2460, 2480, 2488, 2496, 2540, 2568, 2584, 2604, 2634, 2640, 2648, 2664, 2688, 2730, 2736, 2744, 2784, 2824, 2832, 2840, 2848, 2856, 2864, 2916, 2934, 2964, 2984, 3024, 3048, 3096, 3126, 3162, 3168

Offset: 1

Zak Seidov, Mar 10 2011

Asymptotic density 19/63 = 0.301.... - Charles R Greathouse IV, Mar 11 2011

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

Subsequence of A187516 (numbers divisible by at least two of their digits, different and >1).

numdig = 3; Select[Range[3168], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)

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 *)

A187533 Numbers divisible by at least five of their digits, different and >1.

Original entry on oeis.org

27384, 29736, 36792, 37296, 37926, 38472, 46872, 73248, 73962, 78624, 79632, 84672, 92736, 123648, 123864, 123984, 124368, 126384, 129384, 132648, 132864, 132984, 134928, 136248, 136824, 138264, 138624, 139248, 139824, 142368, 143928, 146328, 146832, 148392, 148632, 149328, 149832, 162384, 163248, 163824, 164328, 164832, 167328, 167832, 168432, 172368, 183264, 183624, 184392, 184632, 186432, 189432, 192384, 193248, 193824, 194328

Offset: 1

Zak Seidov, Mar 11 2011

There are 11936 terms < 4*10^6.

Asymptotic density 97/1260 = 0.0769.... - Charles R Greathouse IV, Mar 11 2011

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

Subsequence of A187238.

Cf. A187398, A187516.

numdig = 5; Select[Range[194328], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)

A187534 Numbers divisible by at least six of their digits, different and >1.

Original entry on oeis.org

243768, 247968, 248976, 297864, 364728, 367248, 376824, 427896, 428736, 432768, 469728, 478296, 478632, 483672, 623784, 627984, 634872, 689472, 732648, 742896, 746928, 762384, 768432, 789264, 796824, 824376, 836472, 873264, 897624, 927864, 976248, 978264, 1289736, 1293768, 1369872, 1372896, 1376928, 1382976, 1679328, 1679832

Offset: 1

Zak Seidov, Mar 11 2011

There are 1437 terms < 10^7.

Asymptotic density 1/35 = 0.0285.... - Charles R Greathouse IV, Mar 11 2011

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

Subsequence of A187533.

Cf. A187398, A187516, A187238.

numdig = 6; Select[Range[1679832], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)
Select[Range[2*10^5,168*10^4],Length[Select[#/Union[DeleteCases[IntegerDigits[#],1]],IntegerQ]]>5&]//Quiet (* Harvey P. Dale, Mar 18 2025 *)

A187551 Numbers divisible by at least seven of their digits, different and >1.

Original entry on oeis.org

23469768, 23579640, 23594760, 23674896, 23684976, 23687496, 23745960, 23746968, 23769648, 23796864, 23876496, 23897664, 23947560, 23957640, 23976540, 24367896, 24375960, 24376968, 24539760, 24679368, 24687936, 24753960, 24783696, 24869376, 24876936, 25497360, 25639740, 25749360, 25793460, 25967340

Offset: 1

Zak Seidov, Mar 11 2011

There are 708 terms < 10^8.

Asymptotic density 1/180 = 0.00555.... - Charles R Greathouse IV, Mar 11 2011

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

Subsequence of A187534.

Cf. A187398, A187516, A187238, A187533.

numdig = 7; Select[Range[25967340], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)

A187565 Numbers divisible by at least eight of their digits, different and >1.

Original entry on oeis.org

1234759680, 1234857960, 1234895760, 1234958760, 1235487960, 1235679480, 1235976840, 1236795840, 1237569480, 1237589640, 1237594680, 1237695480, 1237894560, 1238549760, 1238574960, 1238597640, 1238975640, 1239547680, 1239567840, 1239756840, 1239784560, 1239847560, 1239857640, 1243579680, 1243589760, 1243879560, 1243957680, 1245378960, 1245973680, 1245983760

Offset: 1

Zak Seidov, Mar 11 2011

First 11460 terms are pandigital numbers (A050278).
Asymptotic density 1/2520 = 0.000396.... - Charles R Greathouse IV, Mar 11 2011
11460 terms up to 10^10, 299275 terms up to 10^11, 6224794 terms up to 10^12. - Charles R Greathouse IV, Mar 11 2011

David A. Corneth, Table of n, a(n) for n = 1..11460 (terms <= 10^10)

Cf. A050278, A187398, A187516, A187238, A187533, A187534.

Subsequence of A187551 (numbers divisible by at least seven ...).

numdig = 8; Select[Range[1245983760], Length[(u = Union[Select[IntegerDigits[#], #1 > 1 &]])] >= numdig && Plus @@ (Boole@Divisible[#, u]) >= numdig &] (* Amiram Eldar, Aug 30 2020 *)

s(n) = my(res=Set(digits(n)));select(x->x>1,res)
is(n) = my(d=s(n));if(#d < 8, return(0)); sum(i=1, #d, n%d[i]==0) >= 8 \\ David A. Corneth, Aug 30 2020

A139138 Numbers divisible by at least two of their digits.

Original entry on oeis.org

11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 101, 102, 104, 105, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 131, 132, 135, 138, 140, 141, 142, 144, 145, 147, 148, 150, 151, 152, 153, 155, 156, 161, 162

Offset: 1

Jonathan Vos Post, Jun 05 2008

Digits need not be distinct. This may be considered row 2 of an infinite array whose 1st row is A038770. Each such row is a subset of the ones above it.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Alvin Hoover Belt)
Index entries for 10-automatic sequences

Cf. A038770, A187516.

fQ[n_] := Count[Mod[n, Flatten[IntegerDigits[n] /. {0 -> {}}]], 0] > 1; Select[ Range@ 170, fQ] (* Robert G. Wilson v, Jun 23 2014 *)
Select[Range[200],Count[Divisible[#,Select[IntegerDigits[#], #>0&]], True]>1&] (* Harvey P. Dale, Dec 16 2015 *)

from sympy import factorint
def ok(n): return sum(1 for d in map(int, str(n)) if d > 0 and n%d == 0) > 1
print([k for k in range(163) if ok(k)]) # Michael S. Branicky, Nov 12 2021

More terms from Alvin Hoover Belt, Apr 06 2009

Own omission (140) fixed by Alvin Hoover Belt, Apr 18 2009

A185186 Numbers divisible by at least one of their digits other than 1.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 20, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 52, 55, 60, 62, 63, 64, 65, 66, 70, 72, 75, 77, 80, 82, 84, 85, 88, 90, 92, 93, 95, 96, 99, 102, 104, 105, 112, 115, 120, 122, 123, 124, 125, 126, 128, 132

Offset: 1

Zak Seidov, Mar 11 2011

The only primes in the sequence are 2, 3, 5, 7. No repunits are eligible.
Also, an interesting class of non-eligible integers consists of some powers of 2, 3 and 7:
"2, 4, 8-less" powers of 2, 2^m = 1, 16, 65536 with m = 0, 4, 16 (a subsequence of A034293);
"3, 9-less" powers of 3, 3^m = {1, 27, 81, 177147, 1162261467}, with m = {0, 3, 4, 11, 19} (a subsequence of A131629);
"seven-less" powers of 7, 7^m, with m = 0, 2, 3, 4, 7, 16, 22, 24, 39 (see 6th row of A136291 Array read by rows: each row is a sequence of numbers k such that n^k does not contain the digit n).
Asymptotic density 27/35 = 0.771... - Charles R Greathouse IV, Mar 11 2011
The asymptotic density of numbers having a prime digit is 1 for each prime digit. The asymptotic density of numbers being divisible by 2, 3, 5 or 7 is -Sum_{d|210, d>1}((-1)^omega(d) / d) = 27/35. Also, the asymptotic density of numbers divisible by the first n primes is r(n) where r(1) = 1/2 and r(n) = r(n - 1) + (1 - r(n - 1)) / prime(n). - David A. Corneth, May 28 2017

Giovanni Resta, Table of n, a(n) for n = 1..10000

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

digDivQ[n_] := AnyTrue[IntegerDigits[n], # > 1 && Mod[n, #] == 0 &]; Select[Range[200], digDivQ] (* Giovanni Resta, May 27 2017 *)

is(n) = my(d = vecsort(digits(n), , 8), t = 1); while(t<=#d&&d[t] < 2, t++); sum(i=t, #d, n%d[i]==0) > 0 \\ David A. Corneth, May 27 2017

Name edited by Alonso del Arte, May 16 2017

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

cp's OEIS Frontend

A187398 Numbers divisible by at least three of their digits, all different and >1.

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

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A187533 Numbers divisible by at least five of their digits, different and >1.

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A187534 Numbers divisible by at least six of their digits, different and >1.

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A187551 Numbers divisible by at least seven of their digits, different and >1.

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A187565 Numbers divisible by at least eight of their digits, different and >1.

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A139138 Numbers divisible by at least two of their digits.

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A185186 Numbers divisible by at least one of their digits other than 1.

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

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