A369032 LCM-transform of permutation A241909.

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

Offset

1,2

Comments

See comments in A368900.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = 1, for n > 1, a(n) = lcm {1..A241909(n)} / lcm {1..A241909(n-1)}.

a(n) = A014963(A241909(n)). [A241909 satisfies the property S defined in A368900]

Prog

(PARI)
up_to = 2^18;
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); };
A241909(n) = if(1==n||isprime(n), 2^primepi(n), my(f=factor(n), h=1, i, m=1, p=1, k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k, 1]); m *= p^(i-h); h = i; if(f[k, 2]>1, f[k, 2]--, k++)); (p*m));
v369032 = LCMtransform(vector(up_to, i, A241909(i)));
A369032(n) = v369032[n];
(PARI)
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A369032(n) = A014963(A241909(n));

Crossrefs

Cf. A014963, A122111, A368900, A369031, A369033.

Sequence in context: A339874 A134740 A054714 * A235922 A255598 A060324

Adjacent sequences: A369029 A369030 A369031 * A369033 A369034 A369035

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved