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

1,2

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

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.

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

N. J. A. Sloane

Extensions

More terms from Naohiro Nomoto, Jun 28 2001

Status

approved