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

1, 4, 27, 108, 3125, 12500, 84375, 337500, 823543, 3294172, 22235661, 88942644, 2573571875, 10294287500, 69486440625, 277945762500, 285311670611, 1141246682444, 7703415106497, 30813660425988, 302875106592253, 891598970659375, 1211500426369012, 3566395882637500

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

			3^3*5^5 = 84375.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1038 terms from T. D. Noe)
• Daniel Mondot, Table of n, a(n) for n = 1..10000 with factorizations

Crossrefs

Cf. A027748, A048103, A048104, A051674, A072873, A124010.

Programs

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

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

Extensions

More terms from Naohiro Nomoto, Jun 28 2001