A369459 Lexicographically earliest infinite sequence such that a(i) = a(j) => A369458(i) = A369458(j) for all i, j >= 0.

1, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 5, 2, 6, 2, 2, 1, 7, 4, 8, 3, 9, 5, 10, 2, 11, 6, 12, 2, 5, 2, 2, 1, 13, 7, 14, 4, 15, 8, 16, 3, 17, 9, 18, 5, 19, 10, 20, 2, 21, 11, 22, 6, 23, 12, 24, 2, 25, 5, 26, 2, 10, 2, 2, 1, 27, 13, 28, 7, 29, 14, 30, 4, 31, 15, 32, 8, 33, 16, 34, 3, 35, 17, 36, 9, 37, 18, 38, 5, 39, 19, 40, 10, 41, 20, 42, 2

Offset

0,4

Comments

Restricted growth sequence transform of A369458.

For all i, j >= 1:

A003602(i) = A003602(j) => A369467(i) = A369467(j) => a(i) = a(j).

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Formula

For all n > 0, a(n) = a(2*n) = a(A000265(n)).

Prog

(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A000265(n) = (n>>valuation(n, 2));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A369458(n) = A003415(A000265(A163511(n)));
v369459 = rgs_transform(vector(1+up_to, n, A369458(n-1)));
A369459(n) = v369459[1+n];

Crossrefs

Cf. A000265, A003415, A003602, A163511, A369458, A369465, A369467.

Cf. also A369065.

Sequence in context: A124758 A198328 A366790 * A369467 A227277 A071481

Adjacent sequences: A369456 A369457 A369458 * A369460 A369461 A369462

Keyword

nonn

Author

Antti Karttunen, Jan 28 2024

Status

approved