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A318572 Squarefree numbers A005117(k) whose largest prime factor is not A318411(k).

%I A318572 #51 Jan 03 2024 17:18:39
%S A318572 35,55,70,77,95,105,110,115,119,143,154,155,161,165,187,190,203,209,
%T A318572 210,215,221,230,231,235,238,247,253,285,286,287,295,299,310,319,322,
%U A318572 323,329,330,335,345,355,357,371,374,377,385,391,395,403,406,407,413,415,418,429,430
%N A318572 Squarefree numbers A005117(k) whose largest prime factor is not A318411(k).
%H A318572 Seiichi Manyama, <a href="/A318572/b318572.txt">Table of n, a(n) for n = 1..5000</a>
%e A318572 A005117(k) is the k-th squarefree number.
%e A318572 A073482(k) is the largest prime factor of A005117(k).
%e A318572 A073482(k) = A318411(k) for 2 <= k <= 22.
%e A318572 -------+------------+------------+------------
%e A318572     k  | A005117(k) | A073482(k) | A318411(k)
%e A318572 -------+------------+------------+------------
%e A318572     23 |         35 |          7 |         13
%e A318572     34 |         55 |         11 |         21
%e A318572     44 |         70 |          7 |         13
%e A318572     48 |         77 |         11 |         31
%e A318572     60 |         95 |         19 |         37
%e A318572     65 |        105 |          7 |         13
%e A318572     69 |        110 |         11 |         21
%e A318572     73 |        115 |         23 |         45
%e A318572     75 |        119 |         17 |         49
%e A318572     89 |        143 |         13 |         61
%e A318572     94 |        154 |         11 |         31
%e A318572     95 |        155 |         31 |         61
%e A318572     99 |        161 |         23 |         67
%e A318572    101 |        165 |         11 |         21
%e A318572    115 |        187 |         17 |         81
%e A318572    116 |        190 |         19 |         37
%o A318572 (Ruby)
%o A318572 require 'prime'
%o A318572 def A(n)
%o A318572   s = 1
%o A318572   flag = false
%o A318572   while !flag
%o A318572     s += 1
%o A318572     flag = true
%o A318572     (1..n - 1).each{|i|
%o A318572       if i != ((i ** s) % n)
%o A318572         flag = false
%o A318572         break
%o A318572       end
%o A318572     }
%o A318572   end
%o A318572   s
%o A318572 end
%o A318572 def A318572(n)
%o A318572   ary = []
%o A318572   i = 2
%o A318572   while ary.size < n
%o A318572     pq = i.prime_division
%o A318572     if pq.all?{|j| j[1] == 1}
%o A318572       ary << i if A(i) != pq[-1][0]
%o A318572     end
%o A318572     i += 1
%o A318572   end
%o A318572   ary
%o A318572 end
%o A318572 p A318572(50)
%Y A318572 Cf. A005117, A073482, A318411.
%K A318572 nonn
%O A318572 1,1
%A A318572 _Seiichi Manyama_, Aug 29 2018