A328471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328461(i)) = A046523(A328461(j)) for all i, j.

1, 1, 2, 1, 2, 3, 3, 1, 2, 4, 5, 5, 2, 2, 5, 1, 2, 5, 5, 6, 5, 2, 5, 7, 2, 3, 8, 2, 5, 9, 5, 1, 2, 6, 9, 5, 5, 5, 5, 10, 2, 2, 10, 5, 2, 5, 11, 9, 2, 5, 9, 2, 9, 11, 9, 5, 2, 12, 10, 10, 2, 2, 5, 1, 5, 13, 12, 5, 9, 5, 14, 10, 5, 2, 10, 2, 5, 5, 12, 15, 2, 2, 10, 3, 10, 12, 9, 2, 2, 16, 5, 12, 10, 2, 5, 5, 2, 5, 5, 9, 5, 5, 10, 5, 2

Offset: 1

Author

Antti Karttunen, Oct 18 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f(n) = A046523(A276156(n)/A002110(A007814(n))).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A007814, A046523, A276156, A328461, A328472, A328474.

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; };
A002110(n) = prod(i=1,n,prime(i));
A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };
A328461(n) = (A276156(n)/A002110(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
v328471 = rgs_transform(vector(up_to, n, A046523(A328461(n))));
A328471(n) = v328471[n];