A369028 - OEIS

%I #12 Jan 24 2024 18:33:33

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

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,5,1,1,1,7,1,11,13,2,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1

%N Exponential of Mangoldt function permuted by A253563.

%C Also LCM-transform of A253563 (when viewed as an offset-1 sequence), because A253563 has the S-property explained in the comments of A368900.

%H Antti Karttunen, <a href="/A369028/b369028.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(A253563(n)).

%F a(1) = 0, and for n > 0, a(n) = lcm {1..A253563(n)} / lcm {1..A253563(n-1)}. [See comments]

%o (PARI)

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

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));

%o A253560(n) = if(1==n, 1, (n*prime(A061395(n))));

%o A253563(n) = if(n<2,(1+n),if(!(n%2),A253560(A253563(n/2)),A253550(A253563((n-1)/2))));

%o A369028(n) = A014963(A253563(n));

%Y Cf. A014963, A054429, A368900, A369029, A369030, A369053.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 12 2024