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%I A260458 #9 Aug 01 2019 04:10:21
%S A260458 1,4,3,2,5,12,7,2,3,20,11,6,13,28,15,2,17,12,19,10,21,44,23,6,5,52,3,
%T A260458 14,29,60,31,2,33,68,35,6,37,76,39,10,41,84,43,22,15,92,47,6,7,20,51,
%U A260458 26,53,12,55,14,57,116,59,30,61,124,21,2,65,132,67,34
%N A260458 Limit of gcd(PP(n) - k, PP(n) + k) as k -> oo, where PP(n) is the product of the first n primes.
%C A260458 a(n) < n if n is in A013929 (numbers that are not squarefree);
%C A260458 a(n) = n if n is in A008578 (primes at beginning of 20th century);
%C A260458 a(n) > n if n is in A039956 (even squarefree numbers).
%H A260458 Clark Kimberling, <a href="/A260458/b260458.txt">Table of n, a(n) for n = 1..10000</a>
%e A260458 For n = 3:
%e A260458 k    2*3*5-k   2*3*5-k   GCD
%e A260458 1       29       31       1
%e A260458 2       28       32       4
%e A260458 3       27       33       3
%e A260458 4       26       34       2
%e A260458 For n = 4:
%e A260458 k    2*3*5*7-k   2*3*5*7-k   GCD
%e A260458 1       29       31           1
%e A260458 2       28       32           4
%e A260458 3       27       33           3
%e A260458 4       26       34           2
%t A260458 z = 120; f[n_] := f[n] = Product[Prime[k], {k, 1, n}];
%t A260458 t[n_, k_] := t[n, k] = GCD[f[n] - k, f[n] + k];
%t A260458 Table[t[50, k], {k, 1, z}]
%Y A260458 Cf. A000040.
%K A260458 nonn,easy
%O A260458 1,2
%A A260458 _Clark Kimberling_, Sep 17 2015

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