A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 3, 2, 1, 3, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 5, 2, 2, 2, 6, 1, 3, 2, 2, 4, 4, 2, 4, 2, 2, 3, 2, 2, 2, 1, 4, 3, 2, 2, 3, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 3, 2, 2, 5, 7, 2, 4, 2, 8, 2, 2, 6, 5, 1, 2, 3, 2, 2, 9

Offset: 1

Author

Antti Karttunen, Jul 31 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of A336476.

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A000593, A336475, A336476.

Cf. also A003602, A324400, A336320.

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; };
A000593(n) = sigma(n>>valuation(n, 2));
A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
A336476(n) = gcd(A000593(n), A336475(n));
v336648 = rgs_transform(vector(up_to,n,A336476(n)));
A336648(n) = v336648[n];