OFFSET
1,1
COMMENTS
Complement of A048103; A129251(a(n)) > 0; A051674 is a subsequence; A129254 = (terms a(k) such that a(k+1)=a(k)+1). - Reinhard Zumkeller, Apr 07 2007
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ k*n with k = 1/(1 - Product(1 - p^-p)) = 3.5969959469... where the product is over all primes p. - Charles R Greathouse IV, Jan 24 2012
EXAMPLE
54 is included because 3^3 divides 54.
MATHEMATICA
fQ[n_] := Union[ Table[ #[[1]] <= #[[2]]] & /@ FactorInteger[n]][[ -1]] == True; Select[ Range[2, 215], fQ[ # ] &] (* Robert G. Wilson v, Dec 14 2004 *)
f[n_] := Module[{aux=FactorInteger[n]}, Last@Union@Table[aux[[i, 1]] <= aux[[i, 2]], {i, Length[aux]}] == True]; Select[Range[2, 215], f] (* José María Grau Ribas, Jan 25 2012 *)
Rest@ Select[Range@ 216, Times @@ Boole@ Map[First@ # > Last@ # &, FactorInteger@ #] == 0 &] (* Michael De Vlieger, Aug 19 2016 *)
PROG
(PARI) is(n)=forprime(p=2, default(primelimit), if(n%p^p==0, return(1)); if(p^p>n, return(0))) \\ Charles R Greathouse IV, Jan 24 2012
(Haskell)
a100716 n = a100716_list !! (n-1)
a100716_list = filter (\x -> or $
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
(Python)
from itertools import count, islice
from sympy import factorint
def A100716_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:any(map(lambda d:d[1]>=d[0], factorint(n).items())), count(max(startvalue, 1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 10 2004
EXTENSIONS
More terms from Robert G. Wilson v, Dec 14 2004
STATUS
approved