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A369030 Exponential of Mangoldt function permuted by A163511 ("Doudna-permutation mirrored").

%I A369030 #16 Jan 24 2024 18:33:50
%S A369030 1,2,2,3,2,3,1,5,2,3,1,5,1,1,1,7,2,3,1,5,1,1,1,7,1,1,1,1,1,1,1,11,2,3,
%T A369030 1,5,1,1,1,7,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,13,2,3,1,
%U A369030 5,1,1,1,7,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1,1,1,1,1
%N A369030 Exponential of Mangoldt function permuted by A163511 ("Doudna-permutation mirrored").
%C A369030 Also LCM-transform of A163511 (when viewed as an offset-1 sequence), because A163511 has the S-property explained in the comments of A368900, from which this can be obtained by permuting with A054429.
%H A369030 Antti Karttunen, <a href="/A369030/b369030.txt">Table of n, a(n) for n = 0..65537</a>
%H A369030 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A369030 a(n) = A014963(A163511(n)).
%F A369030 a(0) = 1, and for n > 0, a(n) = lcm {1..A163511(n)} / lcm {1..A163511(n-1)}. [See comments]
%F A369030 For n > 0, a(n) = A368900(1+A054429(n)).
%o A369030 (PARI)
%o A369030 A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
%o A369030 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A369030 A369030(n) = A014963(A163511(n));
%o A369030 (PARI)
%o A369030 up_to = 65537;
%o A369030 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 A369030 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A369030 v369030 = LCMtransform(vector(up_to,i,A163511(i-1)));
%o A369030 A369030(n) = v369030[1+n];
%Y A369030 Cf. A014963, A054429, A163511, A365805, A368900, A369028, A369029, A369053.
%K A369030 nonn
%O A369030 0,2
%A A369030 _Antti Karttunen_, Jan 12 2024
%E A369030 Changed offset from 1 to 0 and swapped the main and secondary definitions. - _Antti Karttunen_, Jan 24 2024