A369029 Exponential of Mangoldt function permuted by A253565.

1, 2, 3, 2, 5, 3, 1, 2, 7, 5, 1, 3, 1, 1, 1, 2, 11, 7, 1, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 13, 11, 1, 7, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 17, 13, 1, 11, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Antti Karttunen, Jan 12 2024

Keywords

• nonn

Comments

Also LCM-transform of A253565 (when viewed as an offset-1 sequence), because A253565 has the S-property explained in the comments of A368900.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A014963, A253565, A368900, A369028, A369030, A369053.

Programs

PARI

A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253565(n) = if(n<2,(1+n),if(!(n%2),A253550(A253565(n/2)),A253560(A253565((n-1)/2))));
A369029(n) = A014963(A253565(n));

Formula

a(n) = A014963(A253565(n)).

a(0) = 1, and for n > 0, a(n) = lcm {1..A253565(n)} / lcm {1..A253565(n-1)}. [LCM-transform, see comments]