%I #9 Jan 24 2024 18:33:56

%S 1,2,2,3,3,2,1,5,5,1,2,3,1,1,1,7,7,1,1,1,3,2,1,5,1,1,1,1,1,1,1,11,11,

%T 1,1,1,1,1,1,1,5,1,2,3,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,13,13,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,3,2,1,5,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1

%N Exponential of Mangoldt function permuted by A243353.

%C Also LCM-transform of A243353 (when viewed as an offset-1 sequence), because A243353 has the S-property explained in the comments of A368900.

%H Antti Karttunen, <a href="/A369053/b369053.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A014963(A243353(n)).

%F a(0) = 1, and for n > 0, a(n) = lcm {1..A243353(n)} / lcm {1..A243353(n-1)}. [See comments]

%o (PARI)

%o A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

%o A003188(n) = bitxor(n, n>>1);

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A243353(n) = A005940(1+A003188(n));

%o A369053(n) = A014963(A243353(n));

%Y Cf. A003188, A014963, A243353, A368900, A369028, A369029, A369030.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 12 2024