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A129129
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An irregular triangular array of natural numbers read by rows, with shape sequence A000041(n) related to sequence A060850.
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4
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1, 2, 3, 4, 5, 6, 8, 7, 10, 9, 12, 16, 11, 14, 15, 20, 18, 24, 32, 13, 22, 21, 28, 25, 30, 40, 27, 36, 48, 64, 17, 26, 33, 44, 35, 42, 56, 50, 45, 60, 80, 54, 72, 96, 128, 19, 34, 39, 52, 55, 66, 88, 49, 70, 63, 84, 112, 75, 100, 90, 120, 160, 81, 108, 144, 192, 256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The tree begins
1
2
3 4
5 6 8
7 10 9 12 16
11 14 15 20 18 24 32
...
and hence differs from A114622.
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EXAMPLE
| The array is a tree structure as described by A128628. If a node value has only one branch the value is twice that of its parent node. If it has two branches one is twice that of its parent node but the other is adjusted as indicated below:
(1) pick an odd number (e.g. 135)
(2) calculate its prime factorization ( 135 = 5*3*3*3)
(3) note the least prime factor (LPF(135) = 3
(4) note the index of the LPF (index(3) = 2
(5) subtract one from the index (2-1 =1)
(6) calculate the prime associated with the value in step five (prime(1) = 2)
(7) The parent node generating the odd number 135 is (2/3)*135 = 90.
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CROSSREFS
| Cf. A000040 A114622 A128628.
Sequence in context: A117333 A078840 A185974 * A114622 A125624 A145518
Adjacent sequences: A129126 A129127 A129128 * A129130 A129131 A129132
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KEYWORD
| nonn,tabf
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Mar 31 2007
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