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A370923
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Rectangular array read by antidiagonals: row n shows the numbers m >=2 such that the maximum number of consecutive 0's in (e(1), e(2), ..., e(k)) is n-1, where p(1)^e(1) * p(2)^e(2) * ... * p(k)^e(k) is the prime factorization of m.
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6
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2, 4, 3, 6, 9, 5, 8, 10, 14, 7, 12, 15, 25, 22, 11, 16, 20, 28, 39, 26, 13, 18, 21, 33, 44, 51, 34, 17, 24, 27, 35, 49, 52, 57, 38, 19, 30, 40, 55, 77, 95, 68, 69, 46, 23, 32, 42, 56, 78, 102, 114, 76, 87, 58, 29, 36, 45, 65, 85, 104, 115, 138, 92, 93, 62
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OFFSET
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1,1
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COMMENTS
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Every positive integer >1 occurs exactly once.
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LINKS
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EXAMPLE
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Corner:
2 4 6 8 12 16 18 24 30
3 9 10 15 20 21 27 40 42
5 14 25 28 33 35 55 56 65
7 22 39 44 49 77 78 85 88
11 26 51 52 95 102 104 121 143
13 34 57 68 114 115 136 169 171
17 38 69 76 138 145 152 207 217
19 46 87 92 155 174 184 259 261
23 58 93 116 185 186 232 279 287
29 62 111 124 205 222 248 301 333
31 74 123 148 215 246 296 329 369
37 82 129 164 235 258 328 371 387
22 = 2^1 * 3^0 * 5^0 * 7^0 * (11)^1, so (e(1),e(2),e(3),e(4),e(5)) = (1,0,0,0,1), so 22 is in row 4.
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MATHEMATICA
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Map[Transpose[#][[1]] &, GatherBy[Map[{#, Max[Map[Length, DeleteCases[
Split[Map[IntegerQ, #/Prime[Range[PrimePi[FactorInteger[#][[-1, 1]]]]]] &[#]], {___, True, ___}]] /. {} -> {0}]} &, Range[2, 400]], #[[2]] &]] // ColumnForm
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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