A322808 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = 0 if n is a squarefree number > 2, and f(n) = A097246(n) for all other numbers.

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

Offset: 1

Author

Antti Karttunen, Dec 26 2018

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A097249(i) = A097249(j).

Links

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

Crossrefs

Cf. A005117, A097246, A097249, A305980.

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; };
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i,1]+1)^(f[i,2]\2))*((f[i,1])^(f[i,2]%2))); };
A322808aux(n) = if((n>2)&&issquarefree(n),0,A097246(n));
v322808 = rgs_transform(vector(up_to,n,A322808aux(n)));
A322808(n) = v322808[n];