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A369030
Exponential of Mangoldt function permuted by A163511 ("Doudna-permutation mirrored").
5
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.
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));
(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];
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