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A278028
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Let {c(i)} = A007916 denote the sequence of numbers > 1 which are not perfect powers. Every positive integer n has a unique representation as a tower n = c(x_1)^c(x_2)^c(x_3)^...^c(x_k), where the exponents are nested from the right. The sequence is an irregular triangle read by rows, where the n-th row lists x_1, ..., x_k.
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15
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1, 2, 1, 1, 3, 4, 5, 1, 2, 2, 1, 6, 7, 8, 9, 10, 11, 1, 1, 1, 12, 13, 14, 15, 16, 17, 18, 19, 3, 1, 20, 2, 2, 21, 22, 23, 24, 1, 3, 25, 26, 27, 4, 1, 28, 29, 30, 31
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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Row lengths are A288636(n). - Gus Wiseman, Jun 12 2017
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..20181
N. J. A. Sloane, Maple programs for A007916, A278028, A278029, A052409, A089723, A277564
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EXAMPLE
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Rows 2 through 32 are:
1,
2,
1, 1,
3,
4,
5,
1, 2,
2, 1,
6,
7,
8,
9,
10,
11,
1, 1, 1,
12,
13,
14,
15,
16,
17,
18,
19,
3, 1,
20,
2, 2,
21,
22,
23,
24,
1, 3,
...
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CROSSREFS
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See A277564 for another version.
Cf. A007916, A089723, A277562, A288636.
Sequence in context: A307277 A210691 A262175 * A124424 A057044 A153899
Adjacent sequences: A278025 A278026 A278027 * A278029 A278030 A278031
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Nov 09 2016
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STATUS
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approved
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