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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Jan 12 2024

Keywords

• nonn

Comments

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.

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, A054429, A163511, A365805, A368900, A369028, A369029, A369053.

Programs

PARI

A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
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));
A369030(n) = A014963(A163511(n));

PARI

up_to = 65537;
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); };
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));
v369030 = LCMtransform(vector(up_to,i,A163511(i-1)));
A369030(n) = v369030[1+n];

Formula

a(n) = A014963(A163511(n)).

a(0) = 1, and for n > 0, a(n) = lcm {1..A163511(n)} / lcm {1..A163511(n-1)}. [See comments]

For n > 0, a(n) = A368900(1+A054429(n)).

Extensions

Changed offset from 1 to 0 and swapped the main and secondary definitions. - Antti Karttunen, Jan 24 2024