The OEIS is supported by the many generous donors to the OEIS Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A072103 Sorted perfect powers a^b for a, b > 1 with duplication. 13
 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} Sum_{j>=2} 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 (Python) import numpy from math import isqrt upto = 1090 A072103 = [] for m in range(2, isqrt(upto)+1): k = 2 while m**k < upto: A072103.append(m**k) k += 1 print(sorted(A072103)) # Karl-Heinz Hofmann, Sep 16 2023 CROSSREFS Cf. A001597, A000005, A072103, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 13:14 EST 2023. Contains 367591 sequences. (Running on oeis4.)