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%I #20 Jan 03 2024 07:08:56
%S 1,1,2,1,4,2,6,1,1,4,10,1,12,7,1,3,16,2,18,1,1,10,22,1,2,13,1,1,28,2,
%T 30,1,1,16,2,1,36,19,1,3,40,1,42,1,1,21,46,2,4,4,9,1,52,2,1,1,1,27,58,
%U 1,60,29,2,2,2,1,66,12,1,2,70,1,72,37,2,1,2,1,78,1,1,40,82,1,7,42,2,2,88,2,3
%N a(1) = 1; for n > 1, a(n) is the number of i in range 1..n-1 for which gcd(n, a(i)) = Max_{k=1..n-1} gcd(n, a(k)).
%C a(n) = n-1 iff n = 1 or n is prime;
%C a(A098373(n)) = n and a(m) <> n for m < A098373(n);
%C a(A098374(n)) = 1;
%C a(n) = #{m: gcd(n,a(m)) = A098372(n)}.
%C Notes from _Antti Karttunen_, Mar 30 2021: (Start)
%C The original definition was: #{m: gcd(n, a(m)) = Max_{k=1..n-1} gcd(n, a(k))}, but it hardly seems well-defined unless the range of m is somehow restricted.
%C Informally the definition could be expressed as: Number of k in range 1..n-1 for which gcd(n, a(k)) attains the maximal such gcd-value that occurs in the same range.
%C (End)
%H Antti Karttunen, <a href="/A098371/b098371.txt">Table of n, a(n) for n = 1..8192</a>
%H Antti Karttunen, <a href="/A098371/a098371.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o (PARI) A098371list(up_to) = { my(v=vector(up_to)); v[1] = 1; for(n=2,#v,my(m=1); for(k=1,n-1,m = max(m,gcd(n,v[k]))); v[n] = sum(k=1,n-1,m == gcd(n,v[k]))); (v); }; \\ _Antti Karttunen_, Mar 30 2021
%Y Cf. A096216, A000010, A098372, A098373, A098374.
%K nonn,look
%O 1,3
%A _Reinhard Zumkeller_, Sep 05 2004
%E Definition clarified by _Antti Karttunen_, Mar 30 2021
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