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.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..59.

Example

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.

Sequence in context: A339468 A252019 A377878 * A299206 A153408 A281885

Adjacent sequences: A372256 A372257 A372258 * A372260 A372261 A372262

Keyword

nonn,base,full,fini

Author

Chai Wah Wu, Apr 24 2024

Status

approved