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 A072103 Sorted perfect powers a^b for a, b > 1 with duplication. 10
 4, 8, 9, 16, 16, 25, 27, 32, 36, 49, 64, 64, 64, 81, 81, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 256, 256, 256, 289, 324, 343, 361, 400, 441, 484, 512, 512, 529, 576, 625, 625, 676, 729, 729, 729, 784, 841, 900, 961, 1000, 1024, 1024, 1024, 1089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If b is the largest integer such that n=a^b for some a>1, then n occurs d(b)-1 times in this sequence (where d = A000005 is the number of divisors function). (This includes the case where b=1 and n does not occur in the sequence.) - M. F. Hasler, Jan 25 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..9999, recomputed with new offset by M. F. Hasler, Jan 25 2015 Eric Weisstein's World of Mathematics, Perfect Power FORMULA Sum_{i=2}^{infty} sum_{j=2}^{infty} 1/i^j = 1. EXAMPLE (a,b) = (2,4) and (4,2) both yield 2^4 = 4^2 = 16, therefore 16 is listed twice. Similarly, 64 is listed 3 times since (a,b) = (2,6), (4,3) and (8,2) all yield 64. MAPLE N:= 2000: # to get all entries <= N sort([seq(seq(a^b, b = 2 .. floor(log[a](N))), a = 2 .. floor(sqrt(N)))]); # Robert Israel, Jan 25 2015 MATHEMATICA nn=60; Take[Sort[#[]^#[]&/@Tuples[Range[2, nn], 2]], nn] (* Harvey P. Dale, Oct 03 2012 *) PROG (Haskell) import Data.Set (singleton, findMin, deleteMin, insert) a072103 n = a072103_list !! (n-1) a072103_list = f 9 3 \$ Set.singleton (4, 2) where    f zz z s      | xx < zz   = xx : f zz z (Set.insert (x*xx, x) \$ Set.deleteMin s)      | otherwise = zz : f (zz+2*z+1) (z+1) (Set.insert (z*zz, z) s)      where (xx, x) = Set.findMin s -- Reinhard Zumkeller, Oct 04 2012 (PARI) is_A072103(n)=ispower(n) for(n=1, 999, (e=ispower(n))||next; fordiv(e, d, d>1 && print1(n", ")) \\ M. F. Hasler, Jan 25 2015 CROSSREFS Cf. A001597, A000005, A253641, A253642. Sequence in context: A329728 A141066 A018196 * A004756 A237882 A153034 Adjacent sequences:  A072100 A072101 A072102 * A072104 A072105 A072106 KEYWORD nonn AUTHOR Eric W. Weisstein, Jun 18 2002 EXTENSIONS Offset corrected and examples added by M. F. Hasler, Jan 25 2015 STATUS approved

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)