A366790 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366789(i) = A366789(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 5, 2, 3, 2, 6, 1, 7, 4, 2, 3, 8, 5, 9, 2, 10, 3, 11, 2, 5, 6, 12, 1, 13, 7, 6, 4, 3, 2, 6, 3, 14, 8, 7, 5, 15, 9, 16, 2, 4, 10, 17, 3, 2, 11, 18, 2, 8, 5, 19, 6, 9, 12, 20, 1, 21, 13, 22, 7, 21, 6, 5, 4, 23, 3, 24, 2, 13, 6, 12, 3, 25, 14, 26, 8, 27, 7, 13, 5, 3, 15, 6, 9, 28, 16, 6, 2, 29, 4

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A366789(n), A336158(n)].

For all i, j:

A003602(i) = A003602(j) => a(i) = a(j) => A366388(i) = A366388(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
Aux366790(n) = [A366789(n), A336158(n)];
v366790 = rgs_transform(vector(up_to, n, Aux366790(n)));
A366790(n) = v366790[n];

Crossrefs

Cf. A003602, A336158, A366388, A366789, A366792.

Cf. also A336390, A336470.

Sequence in context: A336390 A124758 A198328 * A369459 A369467 A227277

Adjacent sequences: A366787 A366788 A366789 * A366791 A366792 A366793

Keyword

nonn

Author

Antti Karttunen, Oct 23 2023

Status

approved