A369043 LCM-transform of Blue code (A193231).

1, 3, 2, 5, 2, 1, 7, 1, 1, 1, 13, 1, 11, 3, 2, 17, 2, 1, 19, 1, 1, 23, 1, 1, 31, 29, 1, 3, 1, 1, 5, 1, 1, 1, 7, 1, 1, 53, 1, 1, 61, 1, 1, 1, 1, 1, 59, 1, 1, 1, 2, 1, 1, 1, 37, 1, 1, 1, 47, 1, 41, 43, 1, 1, 1, 1, 1, 1, 3, 83, 1, 1, 1, 89, 1, 1, 1, 1, 1, 1, 1, 71, 1, 1, 2, 1, 67, 1, 1, 1, 73, 1, 79, 1, 1, 1, 103, 101

Offset

1,2

Comments

Blue code, A193231, is a self-inverse permutation related to the binary expansion of n that keeps all the numbers of range [2^k, 2^(1+k)[ in the same range, i.e., for all n >= 1, A000523(A193231(n)) = A000523(n), from which it immediately follows that A193231 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A193231(n)), for n >= 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to binary expansion of n

Formula

a(n) = lcm {1..A193231(n)} / lcm {1..A193231(n-1)}.

a(n) = A014963(A193231(n)). [See comments.]

For n >= 1, Product_{d|n} a(A193231(d)) = n. [Implied by above.]

Prog

(PARI)
up_to = 65537; \\ Checked up to 2^17;
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); };
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) };
v369043 = LCMtransform(vector(up_to, i, A193231(i)));
A369043(n) = v369043[n];
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

Crossrefs

Cf. A014963, A193231, A368900, A369041, A369042, A369044, A369045.

Sequence in context: A088233 A056008 A074830 * A182983 A231146 A287692

Adjacent sequences: A369040 A369041 A369042 * A369044 A369045 A369046

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved