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A294337
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Number of ways to write 2^n as a finite power-tower a^(b^(c^...)) of positive integers greater than one.
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8
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1, 2, 2, 4, 2, 4, 2, 6, 4, 4, 2, 7, 2, 4, 4, 10, 2, 7, 2, 7, 4, 4, 2, 10, 4, 4, 6, 7, 2, 8, 2, 12, 4, 4, 4, 12, 2, 4, 4, 10, 2, 8, 2, 7, 7, 4, 2, 15, 4, 7, 4, 7, 2, 10, 4, 10, 4, 4, 2, 13, 2, 4, 7, 16, 4, 8, 2, 7, 4, 8, 2, 16, 2, 4, 7, 7, 4, 8, 2, 15, 10, 4, 2, 13, 4, 4, 4, 10, 2, 13, 4, 7, 4, 4, 4, 18, 2, 7, 7, 12, 2, 8, 2, 10, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The a(12) = 7 ways are: 2^12, 4^6, 8^4, 8^(2^2), 16^3, 64^2, 4096.
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MATHEMATICA
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a[n_]:=1+Sum[a[g], {g, Rest[Divisors[GCD@@FactorInteger[n][[All, 2]]]]}];
Table[a[2^n], {n, 100}]
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PROG
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(PARI)
\\ Or alternatively, after Mathematica-code as:
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CROSSREFS
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Cf. A001597, A007916, A052409, A052410, A089723, A164336, A277562, A284639, A288636, A294336, A294338, A294339.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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