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A048102 Numbers n such that if n = Product p_i^e_i then p_i=e_i for all i. 9
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

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. A048103, A048104, A051674, A072873.

Sequence in context: A071175 A063262 A156223 * A171469 A267685 A190584

Adjacent sequences:  A048099 A048100 A048101 * A048103 A048104 A048105

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Naohiro Nomoto, Jun 28 2001

STATUS

approved

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Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)