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

0,2

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

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)).

Prog

(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];

Crossrefs

Cf. A014963, A054429, A163511, A365805, A368900, A369028, A369029, A369053.

Sequence in context: A347658 A343387 A083900 * A113517 A278399 A349197

Adjacent sequences: A369027 A369028 A369029 * A369031 A369032 A369033

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Extensions

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

Status

approved