A176558 -id:A176558 - cp's OEIS frontend

A243539 Numbers n such that the list of divisors of n contains 6 distinct digits (in base 10).

18, 24, 30, 32, 40, 42, 48, 52, 63, 64, 81, 86, 87, 92, 98, 105, 106, 128, 130, 134, 146, 147, 148, 158, 176, 186, 188, 198, 200, 201, 203, 222, 235, 246, 247, 248, 249, 255, 259, 264, 278, 286, 310, 314, 322, 327, 328, 329, 330, 332, 334, 338, 346, 351, 357

Offset: 1

Jaroslav Krizek, Jun 19 2014

Numbers n such that A037278(n), A176558(n) and A243360(n) contain 6 distinct digits.

			48 is in sequence because the list of divisors of 48: (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) contains 6 distinct digits (1, 2, 3, 4, 6, 8).

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

Cf. A095048, A037278, A176558, A243360.
Sequences of numbers n such that the list of divisors of n contains k distinct digits for 1 <= k <= 10: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).

[Row n = 1...10000; Column A: A(n) = A095048(n); Column B: B(n) = IF(A(n)=6;A(n)); Arrangement of column B]

Select[Range[400],Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]==6&] (* Harvey P. Dale, Apr 13 2025 *)

A243540 Numbers n such that the list of divisors of n contains 7 distinct digits (in base 10).

Original entry on oeis.org

36, 56, 60, 68, 70, 78, 80, 84, 96, 112, 116, 135, 136, 138, 150, 172, 184, 189, 190, 192, 196, 207, 212, 225, 230, 238, 243, 245, 256, 260, 261, 267, 268, 272, 285, 290, 292, 344, 345, 350, 358, 368, 384, 387, 388, 396, 400, 402, 418, 441, 444, 455, 459, 462

Offset: 1

Jaroslav Krizek, Jun 19 2014

Numbers n such that A037278(n), A176558(n) and A243360(n) contain 7 distinct digits.

			36 is in sequence because the list of divisors of 36: (1, 2, 3, 4, 6, 9, 12, 18, 36) contains 7 distinct digits (1, 2, 3, 4, 6, 8, 9).

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

Cf. A095048, A037278, A176558, A243360.
Sequences of numbers n such that the list of divisors of n contains k distinct digits for 1 <= k <= 10: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).

[Row n = 1...10000; Column A: A(n) = A095048(n); Column B: B(n) = IF(A(n)=7;A(n)); Arrangement of column B]

A243541 Numbers n such that the list of divisors of n contains 8 distinct digits (in base 10).

Original entry on oeis.org

72, 76, 102, 104, 120, 126, 140, 144, 160, 168, 170, 182, 208, 210, 224, 232, 234, 236, 240, 258, 266, 276, 282, 288, 294, 296, 300, 308, 318, 320, 336, 352, 370, 372, 376, 416, 424, 430, 435, 436, 438, 448, 460, 464, 470, 476, 483, 494, 518, 520, 528, 536

Offset: 1

Jaroslav Krizek, Jun 19 2014

Numbers n such that A037278(n), A176558(n) and A243360(n) contain 8 distinct digits.

			72 is in sequence because the list of divisors of 72: (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) contains 8 distinct digits (1, 2, 3, 4, 6, 7, 8, 9).

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A095048, A037278, A176558, A243360.
Sequences of numbers n such that the list of divisors of n contains k distinct digits for 1 <= k <= 10: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).

[Row n = 1 …10000; Column A: A(n) = A095048(n); Column B: B(n) = IF(A(n)=8;A(n)); Arrangement of column B]

Select[Range[600],Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]==8&] (* Harvey P. Dale, Jul 14 2016 *)

A243542 Numbers n such that the list of divisors of n contains 9 distinct digits (in base 10).

Original entry on oeis.org

54, 90, 114, 152, 156, 162, 174, 180, 204, 228, 252, 280, 315, 316, 340, 342, 348, 354, 356, 364, 378, 390, 392, 405, 408, 414, 420, 456, 468, 472, 474, 480, 486, 490, 510, 516, 522, 532, 534, 546, 552, 556, 560, 564, 576, 582, 584, 588, 592, 594, 600, 616

Offset: 1

Jaroslav Krizek, Jun 19 2014

Numbers n such that A037278(n), A176558(n) and A243360(n) contain 9 distinct digits.

			54 is in sequence because the list of divisors of 54: (1, 2, 3, 6, 9, 18, 27, 54) contains 9 distinct digits (1, 2, 3, 4, 5, 6, 7, 8, 9).

Cf. A095048, A037278, A176558, A243360.
Sequences of numbers n such that the list of divisors of n contains k distinct digits for 1 <= k <= 10: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).

[Row n = 1 …10000; Column A: A(n) = A095048(n); Column B: B(n) = IF(A(n)=9;A(n)); Arrangement of column B]

A243543 Smallest number whose list of divisors contains n distinct digits (in base 10).

Original entry on oeis.org

1, 2, 4, 6, 12, 18, 36, 72, 54, 108

Offset: 1

Jaroslav Krizek, Jun 19 2014

Finite sequence with 10 terms.

			a(9) = 54 because 54 is the smallest number whose list of divisors contains 9 distinct digits; the list of divisors of 54: (1, 2, 3, 6, 9, 18, 27, 54) contains 9 distinct digits (1, 2, 3, 4, 5, 6, 7, 8, 9).

Cf. Sequences of numbers n such that list of divisors of n contains k distinct digits: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050.

Cf. also A095048, A037278, A176558, A243360.

A209932 Numbers n such that smallest digit of all divisors of n is 0.

Original entry on oeis.org

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 214, 216, 218, 220, 230, 240, 250, 260, 270, 280, 290, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 312, 315, 318, 320, 321, 324, 327, 330, 340, 350, 360, 370, 380, 390, 400

Offset: 1

Jaroslav Krizek, Mar 20 2012

Also numbers n such that smallest digit of concatenation of all divisors of n (A037278 or A176558) is 0.

Sequence is not the same as A011540, first deviation is at a(41): A011540(41) = 220, a(41) = 214.

			Number 214 is in sequence because smallest digit of all divisors of 214 (1, 2, 107, 214) is 0.

Cf. A209929 (smallest digit of all divisors of n), complement of A209931.

Select[Range[400],Min[Flatten[IntegerDigits/@Divisors[#]]]==0&] (* Harvey P. Dale, Dec 03 2021 *)

Corrected and extended by Harvey P. Dale, Dec 03 2021

A257219 Numbers that have at least one divisor containing the digit 2 in base 10.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108

Offset: 1

Jaroslav Krizek, Apr 20 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 2.
Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.
All even numbers and all numbers which have a digit "2" themselves are trivially in this sequence. The first terms not of this form are the odd multiples of odd numbers between 21 and 29: { 63 = 3*21, 69 = 3*23, 75 = 3*25, 81 = 3*27, 87 = 3*29, 105 = 5*21, 115 = 5*23, 135 = 5*27, 145 = 5*29, ...}. - M. F. Hasler, Apr 22 2015
A011532 (numbers that contain a 2) is a subsequence. - Michel Marcus, May 19 2015

			18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 2.
In the same way all even numbers have the divisor 2 and thus are in this sequence; numbers N in { 20,...,29, 120,...,129, 200,...,299 } have the digit 2 in N which is divisor of itself. - _M. F. Hasler_, Apr 22 2015

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A037278, A176558, A243360, A256824.

[n: n in [1..1000] | [2] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 2] > 0 &] (* Michael De Vlieger, Apr 20 2015 *)

is(n)=!bittest(n,0)||setsearch(Set(digits(n)),2)||fordiv(n,d,setsearch(Set(digits(d)),2)&&return(1)) \\ M. F. Hasler, Apr 22 2015

a(n) ~ n. - Charles R Greathouse IV, Apr 22 2015

A257220 Numbers that have at least one divisor containing the digit 3 in base 10.

Original entry on oeis.org

3, 6, 9, 12, 13, 15, 18, 21, 23, 24, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 45, 46, 48, 51, 52, 53, 54, 57, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 78, 81, 83, 84, 86, 87, 90, 91, 92, 93, 96, 99, 102, 103, 104, 105, 106, 108

Offset: 1

Jaroslav Krizek, Apr 20 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 3.

Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.

			18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 3.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A037278, A176558, A243360, A256824.

[n: n in [1..1000] | [3] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 3] > 0 &] (* Michael De Vlieger, Apr 20 2015 *)

is(n)=fordiv(n,d, if(setsearch(Set(digits(d)),3), return(1))); 0 \\ Charles R Greathouse IV, Apr 30 2015

a(n) ~ n. - Charles R Greathouse IV, Apr 30 2015

A257221 Numbers that have at least one divisor containing the digit 4 in base 10.

Original entry on oeis.org

4, 8, 12, 14, 16, 20, 24, 28, 32, 34, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 54, 56, 60, 64, 68, 70, 72, 74, 76, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 108, 112, 114, 116, 120, 123, 124, 126, 128, 129, 132, 134, 135, 136, 138, 140, 141

Offset: 1

Jaroslav Krizek, Apr 20 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 4.

Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.

			16 is in sequence because the list of divisors of 16: (1, 2, 4, 8, 16) contains digit 4.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A037278, A176558, A243360, A256824.

[n: n in [1..1000] | [4] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]

Select[Range@ 141, Part[Plus @@ DigitCount@ Divisors@ #, 4] > 0 &] (* Michael De Vlieger, Apr 20 2015 *)
Select[Range[200],Count[Flatten[IntegerDigits/@Divisors[#]],4]>0&] (* Harvey P. Dale, May 05 2022 *)

is(n)=fordiv(n,d, if(setsearch(Set(digits(d)),4), return(1))); 0 \\ Charles R Greathouse IV, Apr 30 2015

a(n) ~ n. - Charles R Greathouse IV, Apr 30 2015

A257222 Numbers that have at least one divisor containing the digit 5 in base 10.

Original entry on oeis.org

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 70, 75, 80, 85, 90, 95, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 118, 120, 125, 130, 135, 140, 145, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 165

Offset: 1

Jaroslav Krizek, May 05 2015

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 5.

Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.

			20 is in sequence because the list of divisors of 20: (1, 2, 4, 5, 10, 20) contains digit 5.

Cf. A037278, A176558, A243360, A256824.

[n: n in [1..1000] | [5] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 5] > 0 &]
Select[Range[200],Max[DigitCount[Divisors[#],10,5]]>0&] (* Harvey P. Dale, Sep 15 2018 *)

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 5), return(1))); 0

use ntheory ":all"; for my $n (1..1000) { say $n if scalar(grep {/5/} divisors($n)) } # Dana Jacobsen, May 07 2015

use ntheory ":all"; my @a257222 = grep { scalar(grep {/5/} divisors($)) } 1..1000; # _Dana Jacobsen, May 07 2015

from sympy import divisors
A257222_list = [n for n in range(1,10**3) if '5' in set().union(*(set(str(d)) for d in divisors(n,generator=True)))] # Chai Wah Wu, May 06 2015

a(n) ~ n.

Mathematica and PARI programs with assistance from Michael De Vlieger and Charles R Greathouse IV, respectively.

cp's OEIS Frontend

A243539 Numbers n such that the list of divisors of n contains 6 distinct digits (in base 10).

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A243540 Numbers n such that the list of divisors of n contains 7 distinct digits (in base 10).

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A243541 Numbers n such that the list of divisors of n contains 8 distinct digits (in base 10).

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A243542 Numbers n such that the list of divisors of n contains 9 distinct digits (in base 10).

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A243543 Smallest number whose list of divisors contains n distinct digits (in base 10).

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A209932 Numbers n such that smallest digit of all divisors of n is 0.

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A257219 Numbers that have at least one divisor containing the digit 2 in base 10.

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A257220 Numbers that have at least one divisor containing the digit 3 in base 10.

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