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

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, A369033.

Programs

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));

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]