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%I #12 Jun 23 2024 11:52:18
%S 0,0,1,2,1,3,2,4,1,7,6,1,6,7,11,11,8,10,1,15,4,12,1,8,15,21,15,12,16,
%T 1,10,23,18,1,14,23,29,23,20,22,1,31,6,29,18,27,35,14,31,20,28,1,43,
%U 30,1,26,31,16,45,35,24,45,47,36,1,34,39,16,53,47,26,40,1,59,20,42,1,30,47,65,18
%N Number of k in the range s(1), ..., s(n-1) such that gcd(k, s(n)) > 1, where s = A089088.
%C In the terms studied a(n) = 1 if s(n) is 4 or a prime.
%H Scott R. Shannon, <a href="/A373938/b373938.txt">Table of n, a(n) for n = 0..10000</a>
%H Michael De Vlieger, <a href="/A373938/a373938.png">Log log scatterplot of a(n)</a>, n = 2..2^14.
%e a(5) = 5 as A089088(5) = 8 and 8 shares a factor m > 1 with three previous terms, A089088(1) = 2, A089088(2) = 4, and A089088(3) = 6.
%t nn = 120; s[0] = 1; s[1] = p = 2; s[2] = i = 4; s[3] = j = 6;
%t Do[If[PrimeQ[j/2],
%t k = Prime[p++],
%t k = If[PrimeQ[j], i, j] + 1; While[PrimeQ[k], k++]];
%t Set[{s[n], i, j}, {k, j, k}], {n, 4, nn}];
%t s = Array[s, nn];
%t {0}~Join~Table[Function[{m, w}, Count[w, _?(! CoprimeQ[#, m[[1]]] &)]] @@
%t TakeDrop[#, -1] &@ s[[;; n]], {n, nn}] (* _Michael De Vlieger_, Jun 23 2024 *)
%Y Cf. A089088, A373880, A373390, A064413.
%K nonn
%O 0,4
%A _Scott R. Shannon_, Jun 23 2024
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