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A089579
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Total number of perfect powers > 1 below 10^n.
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7
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3, 11, 39, 123, 365, 1109, 3393, 10489, 32668, 102229, 320988, 1010194, 3184136, 10046919, 31723590, 100216743, 316694003, 1001003330, 3164437423, 10004650116, 31632790242, 100021566155, 316274216760, 1000100055682, 3162493192563, 10000464300849, 31623776828239, 100002154796112
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OFFSET
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1,1
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COMMENTS
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k is a perfect power <=> there exist integers a and b, b > 1, and k = a^b.
Limit_{n->oo} a(n)/sqrt(10^n) = 1.
The four terms which make up the difference between A089580(2) - a(2) are: 16 = 2^4 = 4^2, 64 = 2^6 = 4^3 = 8^2 and 81 = 3^4 = 9^2; one for 16, two for 64 and one for 81 making a total of 4. See A117453.
(End)
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LINKS
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FORMULA
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EXAMPLE
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For n=2, the 11 perfect powers > 1 below 10^2 = 100 are: 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81. - Michael B. Porter, Jul 18 2016
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MATHEMATICA
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Table[lim=10^n-1; Sum[ -(Floor[lim^(1/k)]-1)*MoebiusMu[k], {k, 2, Floor[Log[2, lim]]}], {n, 30}] (* T. D. Noe, Nov 16 2006 *)
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PROG
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(SageMath)
gen = (p for p in srange(2, 10^n) if p.is_perfect_power())
return sum(1 for _ in gen)
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CROSSREFS
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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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