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 A036490 Numbers whose prime factors are in {5, 7, 11}. 3

%I

%S 5,7,11,25,35,49,55,77,121,125,175,245,275,343,385,539,605,625,847,

%T 875,1225,1331,1375,1715,1925,2401,2695,3025,3125,3773,4235,4375,5929,

%U 6125,6655,6875,8575,9317,9625,12005,13475,14641,15125,15625,16807

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

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 160.

%H Reinhard Zumkeller, <a href="/A036490/b036490.txt">Table of n, a(n) for n = 1..1000</a>

%F Sum_{n>=1} 1/a(n) = (5*7*11)/((5-1)*(7-1)*(11-1)) - 1 = 29/48. - _Amiram Eldar_, Sep 24 2020

%F a(n) ~ exp((6*log(5)*log(7)*log(11)*n)^(1/3)) / sqrt(385). - _Vaclav Kotesovec_, Sep 24 2020

%t Select[Range[20000], (fi = FactorInteger[#][[All, 1]]; Intersection[fi, {5, 7, 11}] == fi)&]

%t (* or, for a large number of terms: *)

%t 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 import Data.Set (Set, fromList, insert, deleteFindMin)

%o a036490 n = a036490_list !! (n-1)

%o a036490_list = f \$ fromList [5,7,11] where

%o f s = m : (f \$ insert (5 * m) \$ insert (7 * m) \$ insert (11 * m) s')

%o where (m, s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Feb 19 2013

%Y Cf. A036491, A036492.

%K nonn,easy

%O 1,1

%A _Olivier Gérard_

%E Offset corrected by _Reinhard Zumkeller_, Feb 19 2013

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Last modified November 26 01:22 EST 2020. Contains 338631 sequences. (Running on oeis4.)