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A369033 LCM-transform of permutation A241916.

%I A369033 #13 Jan 30 2024 08:24:10
%S A369033 1,2,3,2,5,3,7,2,1,5,11,3,13,7,1,2,17,1,19,5,1,11,23,3,1,13,1,7,29,1,
%T A369033 31,2,1,17,1,1,37,19,1,5,41,1,43,11,1,23,47,3,1,1,1,13,53,1,1,7,1,29,
%U A369033 59,1,61,31,1,2,1,1,67,17,1,1,71,1,73,37,1,19,1,1,79,5,1,41,83,1,1,43,1,11,89,1,1,23,1,47
%N A369033 LCM-transform of permutation A241916.
%C A369033 See comments in A368900.
%H A369033 Antti Karttunen, <a href="/A369033/b369033.txt">Table of n, a(n) for n = 1..65537</a>
%F A369033 a(1) = 1, for n > 1, a(n) = lcm {1..A241916(n)} / lcm {1..A241916(n-1)}.
%F A369033 a(n) = A014963(A241916(n)). [A241916 satisfies the property S defined in A368900]
%o A369033 (PARI)
%o A369033 up_to = 2^16;
%o A369033 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 A369033 A209229(n) = (n && !bitand(n,n-1));
%o A369033 A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf,1]), g = f); for(i=1,nbf,g[i,1] = prime(1+igp-primepi(f[i,1]))); factorback(g)/2); \\ _Antti Karttunen_, Jan 12 2024
%o A369033 v369033 = LCMtransform(vector(up_to,i,A241916(i)));
%o A369033 A369033(n) = v369033[n];
%o A369033 (PARI)
%o A369033 A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
%o A369033 A369033(n) = A014963(A241916(n));
%Y A369033 Cf. A014963, A122111, A368900, A369031, A369032.
%K A369033 nonn
%O A369033 1,2
%A A369033 _Antti Karttunen_, Jan 12 2024