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A045542
Sub-perfect powers: perfect powers (squares, cubes etc.) minus 1.
33
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
OFFSET
1,1
COMMENTS
Goldbach showed that Sum 1/a(n) = 1, see A214390, A214391.
The only primes in the sequence are 3,7,31,127,... the Mersenne primes (A000668). - Zak Seidov, Dec 08 2011
Repdigits of two or more digits, interpreted in the smallest possible base. E.g., the smallest base for 222 is 3, 222 in base 3 is 26, and 26 is in the sequence. - Franklin T. Adams-Watters, Aug 11 2014
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd edition, p. 66.
LINKS
L. Bibiloni, P. Viader, and J. Paradis, On a Series of Goldbach and Euler, Amer. Math. Monthly, 113 (2006), pp. 206-220.
FORMULA
a(n) = A001597(n + 1) - 1.
MATHEMATICA
f[upto_] := Union[Flatten[Table[n^pwr - 1, {pwr, 2, Log[2, upto+1]}, {n, 2, (upto+1)^(1/pwr)}]]]; f[1763] (* Zak Seidov, Dec 08 2011 *)
Select[Range[2000], GCD@@FactorInteger[#][[All, 2]]>1&]-1 (* Harvey P. Dale, Jan 31 2023 *)
PROG
(Haskell)
a045542 n = a045542_list !! (n-1)
a045542_list = map (subtract 1) $ tail a001597_list
-- Reinhard Zumkeller, Jul 15 2012
(PARI) list(lim)=my(v=List()); for(e=2, logint(lim\=1, 2), for(k=2, sqrtnint(lim, e), listput(v, k^e-1))); Set(v) \\ Charles R Greathouse IV, Aug 26 2015
CROSSREFS
Sequence in context: A105173 A309197 A076683 * A249435 A192120 A031404
KEYWORD
easy,nice,nonn
AUTHOR
William M. Glasgow (billg(AT)wakely.com)
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
STATUS
approved