A336157 Lexicographically earliest infinite sequence such that a(i) = a(j) => A318458(i) = A318458(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 2, 3, 2, 1, 4, 5, 2, 6, 2, 7, 8, 1, 2, 9, 2, 10, 11, 3, 2, 6, 4, 12, 13, 14, 2, 15, 2, 1, 11, 6, 11, 16, 2, 3, 11, 17, 2, 18, 2, 19, 20, 7, 2, 6, 4, 21, 22, 23, 2, 24, 22, 6, 22, 17, 2, 25, 2, 26, 27, 1, 11, 28, 2, 6, 11, 28, 2, 29, 2, 5, 30, 31, 11, 32, 2, 31, 33, 6, 2, 34, 35, 3, 11, 36, 2, 37, 22, 38, 11, 39, 40, 6, 2, 41, 20, 42, 2, 43, 2, 44, 45

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A318458(n), A336158(n)].

For all i, j:

A324400(i) = A324400(j) => a(i) = a(j).

A324401(i) = A324401(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A000265, A046523, A318458, A324400, A324401, A336158.

Cf. A324389, A324530, A324531, A324532 for other similar constructions (also similar by their scatter plots).

Programs

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));
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));
A318458(n) = bitand(n, sigma(n)-n);
Aux336157(n) = [A318458(n), A336158(n)];
v336157 = rgs_transform(vector(up_to, n, Aux336157(n)));
A336157(n) = v336157[n];