cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A370970 Numbers k which have a factorization k = f1*f2*...*fr where the digits of {k, f1, f2, ..., fr} together give 0,1,...,9 exactly once.

Original entry on oeis.org

8596, 8790, 9360, 9380, 9870, 10752, 12780, 14760, 14820, 15628, 15678, 16038, 16704, 17082, 17820, 17920, 18720, 19084, 19240, 20457, 20574, 20754, 21658, 24056, 24507, 25803, 26180, 26910, 27504, 28156, 28651, 30296, 30576, 30752, 31920, 32760, 32890, 34902, 36508, 47320, 58401, 65128, 65821
Offset: 1

Views

Author

N. J. A. Sloane, Apr 13 2024, following emails from Ed Pegg Jr and Hans Havermann. The terms were computed by Hans Havermann

Keywords

Comments

The total number of digits in k, f1, ..., fr is ten, and they are all distinct.

Examples

			The complete list of terms:
 8596 = 2*14*307
 8790 = 2*3*1465
 9360 = 2*4*15*78
 9380 = 2*5*14*67
 9870 = 2*3*1645
10752 = 3*4*896
12780 = 4*5*639
14760 = 5*9*328
14820 = 5*39*76
15628 = 4*3907
15678 = 39*402
16038 = 27*594 = 54*297
16704 = 9*32*58
17082 = 3*5694
17820 = 36*495 = 45*396
17920 = 8*35*64
18720 = 4*5*936
19084 = 52*367
19240 = 8*37*65
20457 = 3*6819
20574 = 6*9*381
20754 = 3*6918
21658 = 7*3094
24056 = 8*31*97
24507 = 3*8169
25803 = 9*47*61
26180 = 4*7*935
26910 = 78*345
27504 = 3*9168
28156 = 4*7039
28651 = 7*4093
30296 = 7*8*541
30576 = 8*42*91
30752 = 4*8*961
31920 = 5*76*84
32760 = 8*45*91
32890 = 46*715
34902 = 6*5817
36508 = 4*9127
47320 = 8*65*91
58401 = 63*927
65128 = 7*9304
65821 = 7*9403

Links

Crossrefs

Cf. A370972, A372106.

A370972 Composite numbers with properties that its digits (which may appear with multiplicity) may not appear in any of its factors (wherein the digits may also appear with multiplicity) and the combined digits of the product and the factors must have at least one of each of the ten digits.

Original entry on oeis.org

8596, 8790, 9360, 9380, 9870, 10752, 10764, 10854, 10968, 11760, 12780, 13608, 13860, 14760, 14780, 14820, 15628, 15678, 16038, 16704, 16920, 17082, 17280, 17340, 17640, 17820, 17920, 18090, 18096, 18690, 18720, 18960, 19068, 19084, 19240, 19440, 19460, 19608, 19740, 19780, 19800, 19980, 20457, 20574, 20748, 20754
Offset: 1

Views

Author

N. J. A. Sloane, Apr 15 2024. Terms were computed by Hans Havermann

Keywords

Comments

See A370970 for another version.
Ed Pegg Jr noted that 1476395008 is the smallest term composed of nine distinct digits. See A372106 for subsequent terms. - Hans Havermann, Apr 19 2024

Examples

			996880 = 2*2*4*5*17*733: 8 and 9 appear twice each in the product. 2, 3, and 7 appear twice each in the factors. The digits in the product are distinct from the digits in the factors and, ignoring the duplicates, we have a combined 9680245173, one of each of the ten digits. -  _Hans Havermann_, Apr 15 2024

References

  • Ed Pegg Jr, Posting to Math-Fun Mailing List, April 2024.

Links

Crossrefs

Cf. A370970, A372106.

A372259 Numbers k which have a factorization k = f_1*f_2*...*f_r where f_i >= 1 and the digits of {k, f_1, f_2, ..., f_r} together give 0,1,...,9 exactly once.

Original entry on oeis.org

4830, 6970, 7056, 7096, 7290, 7690, 7830, 8370, 8596, 8652, 8790, 8970, 9076, 9360, 9370, 9380, 9670, 9706, 9720, 9730, 9870, 10752, 12780, 14760, 14820, 15628, 15678, 16038, 16704, 17082, 17820, 17920, 18720, 19084, 19240, 20457, 20574, 20754, 21658, 24056, 24507, 25803, 26180, 26910, 27504, 28156, 28651, 30296, 30576, 30752, 31920, 32760, 32890, 34902, 36508, 47320, 58401, 65128, 65821
Offset: 1

Views

Author

Chai Wah Wu, Apr 24 2024

Keywords

Comments

A370970 is a subsequence. In contrast to A370970, here the factors f_i are allowed to be equal to 1.

Examples

			The complete list of terms:
  4830 = 1*2*5*7*69
  6970 = 1*2*3485
  7056 = 1*3*24*98 = 1*3*8*294
  7096 = 1*2*3548
  7290 = 1*3*5*486
  7690 = 1*2*3845
  7830 = 1*6*29*45
  8370 = 1*2*9*465
  8596 = 2*14*307
  8652 = 1*4*7*309
  8790 = 2*3*1465
  8970 = 1*26*345
  9076 = 1*2*4538
  9360 = 1*5*24*78 = 2*4*15*78
  9370 = 1*2*4685
  9380 = 2*5*14*67
  9670 = 1*2*4835
  9706 = 1*2*4853
  9720 = 1*3*5*648
  9730 = 1*2*4865
  9870 = 2*3*1645
 10752 = 3*4*896
 12780 = 4*5*639
 14760 = 5*9*328
 14820 = 5*39*76
 15628 = 4*3907
 15678 = 39*402
 16038 = 54*297 = 27*594
 16704 = 9*32*58
 17082 = 3*5694
 17820 = 45*396 = 36*495
 17920 = 8*35*64
 18720 = 4*5*936
 19084 = 52*367
 19240 = 8*37*65
 20457 = 3*6819
 20574 = 6*9*381
 20754 = 3*6918
 21658 = 7*3094
 24056 = 8*31*97
 24507 = 3*8169
 25803 = 9*47*61
 26180 = 4*7*935
 26910 = 78*345
 27504 = 3*9168
 28156 = 4*7039
 28651 = 7*4093
 30296 = 7*8*541
 30576 = 8*42*91
 30752 = 4*8*961
 31920 = 5*76*84
 32760 = 8*45*91
 32890 = 46*715
 34902 = 6*5817
 36508 = 4*9127
 47320 = 8*65*91
 58401 = 63*927
 65128 = 7*9304
 65821 = 7*9403

Crossrefs

Cf. A370970, A370972, A372106.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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