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A318199
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a(n) is the largest integer m such that m^n <= n^prime(n).
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2
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1, 2, 6, 11, 34, 48, 112, 139, 274, 794, 860, 2125, 3259, 3313, 4842, 9741, 18637, 17946, 32306, 41558, 39471, 66148, 82046, 131305, 265464, 313781, 288660, 339008, 313761, 366288, 1287573, 1451134, 2014343, 1824089, 3743848, 3371509, 4510880, 5976406
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OFFSET
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1,2
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COMMENTS
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The sequence is not monotonic, for example a(18) < a(17).
Conjecture: there is no run of consecutive increasing terms with more than 17 terms.
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LINKS
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FORMULA
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a(n) = floor(n^(prime(n)/n)).
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MAPLE
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Digits:= 2000:
a:= n-> floor(n^(ithprime(n)/n)):
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MATHEMATICA
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a[n_]:=Floor[n^(Prime[n]/n)]; Array[a, 40]
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PROG
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(PARI) a(n) = sqrtnint(n^prime(n), n); \\ Michel Marcus, Mar 12 2020
vector(40, n, a(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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