OFFSET
1,2
COMMENTS
If a(n) = Product p_i^e_i then p_i > e_i for all i.
Density is 0.72199023441955... = Product_{p>=2} (1 - p^-p) where p runs over the primes. [Charles R Greathouse IV, Jan 25 2012]
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ kn with k = 1/Product_{p>=2}(1 - p^-p) = Product_{p>=2}(1 + 1/(p^p - 1)) = 1.3850602852..., where the product is over all primes p. [Charles R Greathouse IV, Jan 25 2012]
EXAMPLE
6 = 2^1 * 3^1 is OK but 12 = 2^2 * 3^1 is not.
625 = 5^4 is present because it is not divisible by 5^5.
MATHEMATICA
{1}~Join~Select[Range@ 120, Times @@ Boole@ Map[First@ # > Last@ # &, FactorInteger@ #] > 0 &] (* Michael De Vlieger, Aug 19 2016 *)
PROG
(Haskell)
a048103 n = a048103_list !! (n-1)
a048103_list = filter (\x -> and $
zipWith (>) (a027748_row x) (map toInteger $ a124010_row x)) [1..]
-- Reinhard Zumkeller, Apr 28 2012
(Scheme, with Antti Karttunen's IntSeq-library)
;; Antti Karttunen, Aug 18 2016
(PARI) isok(n) = my(f=factor(n)); for (i=1, #f~, if (f[i, 1] <= f[i, 2], return(0))); return(1); \\ Michel Marcus, Nov 13 2020
(Python)
from itertools import count, islice
from sympy import factorint
def A048103_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:all(map(lambda d:d[1]<d[0], factorint(n).items())), count(max(startvalue, 1)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Apr 22 2000
STATUS
approved