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