OFFSET
1,1
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
FORMULA
Sum_{n>=1} 1/a(n) = (5*7*11)/((5-1)*(7-1)*(11-1)) - 1 = 29/48. - Amiram Eldar, Sep 24 2020
a(n) ~ exp((6*log(5)*log(7)*log(11)*n)^(1/3)) / sqrt(385). - Vaclav Kotesovec, Sep 24 2020
MATHEMATICA
Select[Range[20000], (fi = FactorInteger[#][[All, 1]]; Intersection[fi, {5, 7, 11}] == fi)&]
(* or, for a large number of terms: *)
f[pp_(* primes *), max_(* maximum term *)] := Module[{a, aa, k, iter}, k = Length[pp]; aa = Array[a, k]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; A036490 = f[{5, 7, 11}, 2*10^14] // Rest (* Jean-François Alcover, Sep 19 2012, updated Nov 12 2016 *)
PROG
(Haskell)
import Data.Set (Set, fromList, insert, deleteFindMin)
a036490 n = a036490_list !! (n-1)
a036490_list = f $ fromList [5, 7, 11] where
f s = m : (f $ insert (5 * m) $ insert (7 * m) $ insert (11 * m) s')
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Feb 19 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Feb 19 2013
STATUS
approved