A350067 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A342666(n), A350063(n)] for n > 1, with f(1) = 1.

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

Offset: 1

Author

Antti Karttunen, Jan 29 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A342666(n), A350063(n)], when assuming that A342666(1) = 0.

Restricted growth sequence transform of the function f(1) = 0, f(n) = A336470(A156552(n)) for n > 1.

For all i, j >= 1: A305897(i) = A305897(j) => a(i) = a(j) => A350065(i) = A350065(j).

For all i, j >= 2: a(i) = a(j) => A342651(i) = A342651(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A156552, A322993, A336466, A342666, A350063, A336470.

Cf. also A305897, A350065, A342651.

Programs

PARI

up_to = 3003;
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));
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
Aux350067(n) = if(1==n,1,my(u=A000265(A156552(n))); [A046523(u),A336466(u)]);
v350067 = rgs_transform(vector(up_to, n, Aux350067(n)));
A350067(n) = v350067[n];