A322314 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A322312(i) = A322312(j), for all i, j.

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

Offset: 1

Author

Antti Karttunen, Dec 03 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A322312(n)].

Links

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

Crossrefs

Cf. A046523, A322312, 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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A322312(n) = { my(m=1,p); fordiv(n,d,p=1+d; if(isprime(p), for(i=0,oo,if(n%(p^i),m *= prime(i);break)))); (m); };
v322314 = rgs_transform(vector(up_to, n, [A046523(n), A322312(n)]));
A322314(n) = v322314[n];