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A369060 LCM-transform of Sycamore's D(3) variant of Doudna sequence (A356867).

%I A369060 #9 Jan 13 2024 16:13:53
%S A369060 1,2,3,5,2,1,1,2,3,7,1,1,5,1,1,1,2,1,1,1,1,5,1,1,1,2,3,11,1,1,1,1,1,1,
%T A369060 1,1,7,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,2,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,
%U A369060 1,1,1,1,1,1,1,5,1,1,1,2,3,13,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A369060 LCM-transform of Sycamore's D(3) variant of Doudna sequence (A356867).
%C A369060 See discussion at A368900.
%H A369060 Antti Karttunen, <a href="/A369060/b369060.txt">Table of n, a(n) for n = 1..19683</a>
%F A369060 a(n) = lcm {1..A356867(n)} / lcm {1..A356867(n-1)}.
%F A369060 a(n) = A014963(A356867(n)). [This holds because A356867 satisfies the property S explained in A368900]
%o A369060 (PARI)
%o A369060 up_to = 3^9; \\ Checked up to (3^12)
%o A369060 A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==sumdigits(i,3), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };
%o A369060 v356867 = A356867list(up_to);
%o A369060 A356867(n) = v356867[n];
%o A369060 LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2,len, g[n] = lcm(g[n-1],v[n]); b[n] = g[n]/g[n-1]); (b); };
%o A369060 v369060 = LCMtransform(v356867);
%o A369060 A369060(n) = v369060[n];
%o A369060 A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
%Y A369060 Cf. A014963, A356867, A368900.
%K A369060 nonn
%O A369060 1,2
%A A369060 _Antti Karttunen_, Jan 13 2024