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

Author

Antti Karttunen, Jan 12 2024

Keywords

• nonn

Comments

See comments in A368900.

Links

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

Crossrefs

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

Programs

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));

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]