A369044 - OEIS

A369044

LCM-transform of bijective bit reverse (A057889).

1, 2, 3, 2, 5, 1, 7, 2, 3, 1, 13, 1, 11, 1, 1, 2, 17, 1, 5, 1, 1, 1, 29, 1, 19, 1, 3, 1, 23, 1, 31, 2, 1, 1, 7, 1, 41, 1, 1, 1, 37, 1, 53, 1, 1, 1, 61, 1, 1, 1, 1, 1, 43, 1, 59, 1, 1, 1, 1, 1, 47, 1, 1, 2, 1, 1, 97, 1, 3, 1, 113, 1, 73, 1, 1, 1, 89, 1, 11, 1, 1, 1, 101, 1, 1, 1, 1, 1, 1, 1, 109, 1, 1, 1, 5, 1, 67

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OFFSET

1,2

COMMENTS

Bijective bit reverse, A057889, is a 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(A057889(n)) = A000523(n), from which it immediately follows that A057889 has the property S mentioned in the comments of A368900, and therefore this sequence is equal to A014963(A057889(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..A057889(n)} / lcm {1..A057889(n-1)}.

a(n) = A014963(A057889(n)). [See comments.]

For n >= 1, Product_{d|n} a(A057889(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); };

A030101(n) = if(n<1, 0, subst(Polrev(binary(n)), x, 2));

A057889(n) = if(!n, n, A030101(n/(2^valuation(n, 2))) * (2^valuation(n, 2)));

v369044 = LCMtransform(vector(up_to, i, A057889(i)));

A369044(n) = v369044[n];

A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

CROSSREFS

Cf. A000523, A014963, A057889, A368900, A369041, A369042, A369043, A369045.

Sequence in context: A086847 A098228 A081303 * A164880 A374196 A267068

Adjacent sequences: A369041 A369042 A369043 * A369045 A369046 A369047

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 12 2024

STATUS

approved