A336160 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335915(i) = A335915(j) and A336158(i) = A336158(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A335915(n), A336158(n)].

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A336161(i) = A336161(j).

Links

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

Crossrefs

Cf. A000265, A046523, A324400, A335915, A336158, A336159, A336161, A336162.

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));
A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
Aux336160(n) = [A335915(n), A336158(n)];
v336160 = rgs_transform(vector(up_to, n, Aux336160(n)));
A336160(n) = v336160[n];