cp's OEIS Frontend

A036490 Numbers whose prime factors are in {5, 7, 11}.

%I A036490 #24 Sep 24 2020 04:04:10
%S A036490 5,7,11,25,35,49,55,77,121,125,175,245,275,343,385,539,605,625,847,
%T A036490 875,1225,1331,1375,1715,1925,2401,2695,3025,3125,3773,4235,4375,5929,
%U A036490 6125,6655,6875,8575,9317,9625,12005,13475,14641,15125,15625,16807
%N A036490 Numbers whose prime factors are in {5, 7, 11}.
%D A036490 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.
%H A036490 Reinhard Zumkeller, <a href="/A036490/b036490.txt">Table of n, a(n) for n = 1..1000</a>
%F A036490 Sum_{n>=1} 1/a(n) = (5*7*11)/((5-1)*(7-1)*(11-1)) - 1 = 29/48. - _Amiram Eldar_, Sep 24 2020
%F A036490 a(n) ~ exp((6*log(5)*log(7)*log(11)*n)^(1/3)) / sqrt(385). - _Vaclav Kotesovec_, Sep 24 2020
%t A036490 Select[Range[20000], (fi = FactorInteger[#][[All, 1]]; Intersection[fi, {5, 7, 11}] == fi)&]
%t A036490 (* or, for a large number of terms: *)
%t A036490 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 *)
%o A036490 (Haskell)
%o A036490 import Data.Set (Set, fromList, insert, deleteFindMin)
%o A036490 a036490 n = a036490_list !! (n-1)
%o A036490 a036490_list = f $ fromList [5,7,11] where
%o A036490    f s = m : (f $ insert (5 * m) $ insert (7 * m) $ insert (11 * m) s')
%o A036490          where (m, s') = deleteFindMin s
%o A036490 -- _Reinhard Zumkeller_, Feb 19 2013
%Y A036490 Cf. A036491, A036492.
%K A036490 nonn,easy
%O A036490 1,1
%A A036490 _Olivier Gérard_
%E A036490 Offset corrected by _Reinhard Zumkeller_, Feb 19 2013