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A045542
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Sub-perfect powers: perfect powers (squares, cubes etc.) minus 1.
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9
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3, 7, 8, 15, 24, 26, 31, 35, 48, 63, 80, 99, 120, 124, 127, 143, 168, 195, 215, 224, 242, 255, 288, 323, 342, 360, 399, 440, 483, 511, 528, 575, 624, 675, 728, 783, 840, 899, 960, 999, 1023, 1088, 1155, 1224, 1295, 1330, 1368, 1443, 1520, 1599, 1680, 1727
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Goldbach showed that Sum 1/a(n) = 1, see A214390, A214391.
The only primes in the sequence are 3,7,31,127,.. - Mersenne primes (A000668) - Moshe Levin, Dec 08 2011
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REFERENCES
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L. Bibiloni, P. Viader, and J. Paradis, On a Series of Goldbach and Euler, Amer. Math. Monthly, 113 (2006), pp. 206-220.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd edition, p. 66.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
L. Bibiloni, P. Viader, and J. Paradis, On a Series of Goldbach and Euler
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FORMULA
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a(n) = A001597(n + 1) - 1.
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MATHEMATICA
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f[upto_] := Union[Flatten[Table[n^pwr - 1, {pwr, 2, Log[2, upto+1]}, {n, 2, (upto+1)^(1/pwr)}]]]; f[1763] (* Moshe Levin, Dec 08 2011 *)
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PROG
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(Haskell)
a045542 n = a045542_list !! (n-1)
a045542_list = map (subtract 1) $ tail a001597_list
-- Reinhard Zumkeller, Jul 15 2012
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CROSSREFS
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Cf. A000668, A001597.
Sequence in context: A051211 A105173 A076683 * A192120 A031404 A105263
Adjacent sequences: A045539 A045540 A045541 * A045543 A045544 A045545
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KEYWORD
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easy,nice,nonn
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AUTHOR
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William M. Glasgow (billg(AT)wakely.com)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
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STATUS
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approved
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