A369045 LCM-transform of binary invert permutation (A054429).

1, 3, 2, 7, 1, 5, 2, 1, 1, 13, 1, 11, 1, 3, 2, 31, 1, 29, 1, 3, 1, 5, 1, 23, 1, 1, 1, 19, 1, 17, 2, 1, 1, 61, 1, 59, 1, 1, 1, 1, 1, 53, 1, 1, 1, 7, 1, 47, 1, 1, 1, 43, 1, 41, 1, 1, 1, 37, 1, 1, 1, 1, 2, 127, 1, 5, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 113, 1, 1, 1, 109, 1, 107, 1, 1, 1, 103, 1, 101, 1, 1, 1, 97, 1, 1, 1

Offset

1,2

Comments

Binary invert permutation, A054429, 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(A054429(n)) = A000523(n), from which it immediately follows that A054429 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A054429(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..A054429(n)} / lcm {1..A054429(n-1)}.

a(n) = A014963(A054429(n)). [See comments.]

For n >= 1, Product_{d|n} a(A054429(d)) = n. [Implied by above.]

Prog

(PARI)
up_to = 65537;
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); };
A054429(n) = ((3<<#binary(n\2))-n-1);
v369045 = LCMtransform(vector(up_to, i, A054429(i)));
A369045(n) = v369045[n];
(PARI)
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A054429(n) = ((3<<#binary(n\2))-n-1);
A369045(n) = A014963(A054429(n));

Crossrefs

Cf. A014963, A054429, A368900, A369041, A369042, A369043, A369044.

Sequence in context: A318436 A369042 A243375 * A163659 A348337 A010760

Adjacent sequences: A369042 A369043 A369044 * A369046 A369047 A369048

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved