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A369032 LCM-transform of permutation A241909.

%I A369032 #12 Jan 30 2024 08:24:04
%S A369032 1,2,2,3,2,3,2,5,1,3,2,5,2,3,1,7,2,1,2,5,1,3,2,7,1,3,1,5,2,1,2,11,1,3,
%T A369032 1,1,2,3,1,7,2,1,2,5,1,3,2,11,1,1,1,5,2,1,1,7,1,3,2,1,2,3,1,13,1,1,2,
%U A369032 5,1,1,2,1,2,3,1,5,1,1,2,11,1,3,2,1,1,3,1,7,2,1,1,5,1,3,1,13,2,1,1,1,2,1,2,7,1
%N A369032 LCM-transform of permutation A241909.
%C A369032 See comments in A368900.
%H A369032 Antti Karttunen, <a href="/A369032/b369032.txt">Table of n, a(n) for n = 1..65537</a>
%F A369032 a(1) = 1, for n > 1, a(n) = lcm {1..A241909(n)} / lcm {1..A241909(n-1)}.
%F A369032 a(n) = A014963(A241909(n)). [A241909 satisfies the property S defined in A368900]
%o A369032 (PARI)
%o A369032 up_to = 2^18;
%o A369032 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 A369032 A241909(n) = if(1==n||isprime(n),2^primepi(n),my(f=factor(n),h=1,i,m=1,p=1,k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k,1]); m *= p^(i-h); h = i; if(f[k,2]>1, f[k,2]--, k++)); (p*m));
%o A369032 v369032 = LCMtransform(vector(up_to,i,A241909(i)));
%o A369032 A369032(n) = v369032[n];
%o A369032 (PARI)
%o A369032 A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
%o A369032 A369032(n) = A014963(A241909(n));
%Y A369032 Cf. A014963, A122111, A368900, A369031, A369033.
%K A369032 nonn
%O A369032 1,2
%A A369032 _Antti Karttunen_, Jan 12 2024