A322311 Lexicographically earliest such sequence a that a(i) = a(j) => A322310(i) = A322310(j) for all i, j.

1, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 3, 3, 9, 3, 5, 3, 10, 3, 7, 3, 11, 3, 3, 3, 7, 3, 7, 3, 12, 3, 3, 3, 13, 3, 3, 3, 14, 3, 5, 3, 2, 3, 7, 3, 15, 3, 3, 3, 7, 3, 7, 3, 2, 3, 7, 3, 16, 3, 3, 3, 17, 3, 7, 3, 3, 3, 7, 3, 18, 3, 3, 3, 3, 3, 7, 3, 19, 3, 7, 3, 20, 3, 3, 3, 8, 3, 3, 3, 2, 3, 3, 3, 21, 3, 3, 3, 5, 3, 7, 3, 2, 3

Offset: 1

Author

Antti Karttunen, Dec 03 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A322310.

For all i, j: a(i) = a(j) => A014197(i) = A014197(j).

Links

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

Crossrefs

Cf. A014197, A320000, A322310, A322313.

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; };
A320000sq(n, k) = if(1==n, if(1==k,2,1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ Cf. A320000
A322310(n) = if(1==n,3,my(m=1); fordiv(n,d, my(s, p=d+1, q=n/d); if(isprime(p) && (s = sum(i=0,valuation(n, p), A320000sq(q/(p^i),p))), m *= prime(s))); (m));
v322311 = rgs_transform(vector(up_to, n, A322310(n)));
A322311(n) = v322311[n];