A336470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 5, 2, 3, 3, 6, 1, 2, 4, 7, 2, 8, 5, 9, 2, 4, 3, 10, 3, 11, 6, 12, 1, 13, 2, 8, 4, 7, 7, 8, 2, 5, 8, 14, 5, 15, 9, 16, 2, 17, 4, 6, 3, 18, 10, 13, 3, 19, 11, 20, 6, 12, 12, 21, 1, 8, 13, 22, 2, 23, 8, 24, 4, 7, 7, 15, 7, 25, 8, 26, 2, 27, 5, 28, 8, 6, 14, 29, 5, 9, 15, 19, 9, 25, 16, 19, 2, 3, 17, 30, 4, 31, 6, 32, 3, 33

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A336466(n), A336158(n)].

For all i, j:

A336460(i) = A336460(j) => a(i) = a(j),

a(i) = a(j) => A329697(i) = A329697(j),

a(i) = a(j) => A336471(i) = A336471(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));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-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));
Aux336470(n) = [A336466(n), A336158(n)];
v336470 = rgs_transform(vector(up_to, n, Aux336470(n)));
A336470(n) = v336470[n];

Crossrefs

Cf. A336158, A336466.

Cf. also A329697, A336160, A336471.

Sequence in context: A366605 A133755 A357853 * A351093 A070104 A131085

Adjacent sequences: A336467 A336468 A336469 * A336471 A336472 A336473

Keyword

nonn

Author

Antti Karttunen, Jul 24 2020

Status

approved