login
A048102
Numbers k such that if k = Product p_i^e_i then p_i = e_i for all i.
15
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)
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
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Naohiro Nomoto, Jun 28 2001
STATUS
approved