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 A048102 Numbers k such that if k = Product p_i^e_i then p_i=e_i for all i. 12
 1, 4, 27, 108, 3125, 12500, 84375, 337500, 823543, 3294172, 22235661, 88942644, 2573571875, 10294287500, 69486440625, 277945762500, 285311670611, 1141246682444, 7703415106497, 30813660425988, 302875106592253, 891598970659375, 1211500426369012 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS T. D. Noe, Table of n, a(n) for n = 1..1038 FORMULA A027748(a(n),k) = A124010(a(n),k) for k = 1 .. A001221(a(n)). - Reinhard Zumkeller, Jan 21 2012 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/p^p) = 1.2967126856... - Amiram Eldar, Oct 13 2020 EXAMPLE 3^3*5^5 = 84375. MATHEMATICA s=Subsets[{2, 3, 5, 7, 11, 13, 17}]; t={}; Do[u=s[[n]]; AppendTo[t, Product[u[[i]]^u[[i]], {i, 1, Length[u]}]], {n, Length[s]}]; Select[Union[t], #<19^19&] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *) PROG (Haskell) import Data.Set (empty, fromList, deleteFindMin, union) import qualified Data.Set as Set (null, map) a048102 n = a048102_list !! (n-1) a048102_list = 1 : f empty [1] a051674_list where   f s ys pps'@(pp:pps)     | Set.null s = f (fromList (map (* pp) ys)) (pp:ys) pps     | pp < m     = f (s `union` Set.map (* pp) s `union`                       fromList (map (* pp) ys)) ys pps     | otherwise  = m : f s' (m:ys) pps'     where (m, s') = deleteFindMin s -- Reinhard Zumkeller, Jan 21 2012 (PARI) isok(n) = my(f = factor(n)); for (k=1, #f~, if (f[k, 1] != f[k, 2], return(0))); 1; \\ Michel Marcus, Apr 29 2016 CROSSREFS Cf. A027748, A048103, A048104, A051674, A072873, A124010. Sequence in context: A352331 A063262 A156223 * A171469 A267685 A190584 Adjacent sequences:  A048099 A048100 A048101 * A048103 A048104 A048105 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Naohiro Nomoto, Jun 28 2001 STATUS approved

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Last modified July 1 22:23 EDT 2022. Contains 354984 sequences. (Running on oeis4.)