A358747 Lexicographically earliest infinite sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A007814(n), A007949(n), A324198(n)] when n > 1, with f(1) = 1.

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 2, 11, 12, 5, 13, 5, 14, 3, 2, 5, 15, 16, 2, 17, 4, 5, 6, 5, 18, 3, 2, 19, 20, 5, 2, 3, 21, 5, 22, 5, 4, 23, 2, 5, 24, 19, 25, 3, 4, 5, 26, 27, 28, 3, 2, 5, 10, 5, 2, 29, 30, 5, 6, 5, 4, 3, 31, 5, 32, 5, 2, 33, 4, 19, 6, 5, 34, 35, 2, 5, 36, 27, 2, 3, 7, 5, 13, 19, 4, 3, 2, 5, 37, 5, 38, 8, 14, 5, 6, 5, 7, 39

Offset: 1

Author

Antti Karttunen, Dec 01 2022

Keywords

• nonn
• look

Comments

For all i, j: A305900(i) = A305900(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A007814, A007949, A324198.

Cf. also A305900, A358230.

Programs

PARI

up_to = 100000;
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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
Aux358747(n) = if(1==n,n,[A007814(n), A007949(n), A324198(n)]);
v358747 = rgs_transform(vector(up_to, n,Aux358747(n)));
A358747(n) = v358747[n];