A369033 LCM-transform of permutation A241916.

1, 2, 3, 2, 5, 3, 7, 2, 1, 5, 11, 3, 13, 7, 1, 2, 17, 1, 19, 5, 1, 11, 23, 3, 1, 13, 1, 7, 29, 1, 31, 2, 1, 17, 1, 1, 37, 19, 1, 5, 41, 1, 43, 11, 1, 23, 47, 3, 1, 1, 1, 13, 53, 1, 1, 7, 1, 29, 59, 1, 61, 31, 1, 2, 1, 1, 67, 17, 1, 1, 71, 1, 73, 37, 1, 19, 1, 1, 79, 5, 1, 41, 83, 1, 1, 43, 1, 11, 89, 1, 1, 23, 1, 47

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..A241916(n)} / lcm {1..A241916(n-1)}.

a(n) = A014963(A241916(n)). [A241916 satisfies the property S defined in A368900]

Prog

(PARI)
up_to = 2^16;
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); };
A209229(n) = (n && !bitand(n, n-1));
A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf, 1]), g = f); for(i=1, nbf, g[i, 1] = prime(1+igp-primepi(f[i, 1]))); factorback(g)/2); \\ Antti Karttunen, Jan 12 2024
v369033 = LCMtransform(vector(up_to, i, A241916(i)));
A369033(n) = v369033[n];
(PARI)
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A369033(n) = A014963(A241916(n));

Crossrefs

Cf. A014963, A122111, A368900, A369031, A369032.

Sequence in context: A086281 A097975 A130088 * A078834 A039634 A078833

Adjacent sequences: A369030 A369031 A369032 * A369034 A369035 A369036

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved