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A089580
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Total number of perfect powers > 1 below 10^n, counting multiple representations separately.
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6
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3, 15, 49, 143, 406, 1174, 3507, 10674, 32965, 102716, 321797, 1011533, 3186389, 10050743, 31730134, 100228040, 316713623, 1001037546, 3164497349, 10004755374, 31632975598, 100021893194, 316274794666, 1000101078148, 3162495003352, 10000467510247, 31623782520064, 100002164895587
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OFFSET
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1,1
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COMMENTS
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a(n) ~ sqrt(10^n).
The four terms which make up the difference a(2) - A089579(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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16 = 2^4 = 4^2 counts double, 256 = 2^8 = 4^4 = 16^2 counts three times.
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MATHEMATICA
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Table[lim=10^n-1; Sum[Floor[lim^(1/k)]-1, {k, 2, Floor[Log[2, lim]]}], {n, 30}] (* T. D. Noe, Nov 16 2006 *)
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PROG
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(Python) # see link.
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CROSSREFS
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Cf. A089579 (counting multiple representations only once).
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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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