A322810 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 an odd squarefree number > 1, and f(n) = n for all other numbers.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 14, 3, 15, 16, 17, 18, 19, 3, 20, 3, 21, 3, 22, 3, 23, 3, 24, 3, 25, 3, 26, 3, 27, 28, 29, 3, 30, 31, 32, 3, 33, 3, 34, 3, 35, 3, 36, 3, 37, 3, 38, 39, 40, 3, 41, 3, 42, 3, 43, 3, 44, 3, 45, 46, 47, 3, 48, 3, 49, 50, 51, 3, 52, 3, 53, 3, 54, 3, 55, 3, 56, 3, 57, 3, 58, 3, 59, 60, 61, 3, 62, 3, 63, 3

Offset: 1

Author

Antti Karttunen, Dec 27 2018

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A305980(i) = A305980(j),

a(i) = a(j) => A322808(i) = A322808(j).

Links

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

Crossrefs

Cf. A305801, A305980, A322808.

Cf. A056911 (after the initial 1, gives the positions of 3's in this sequence).

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; };
A322810aux(n) = if((n>1)&&(n%2)&&issquarefree(n),0,n);
v322810 = rgs_transform(vector(up_to,n,A322810aux(n)));
A322810(n) = v322810[n];

Formula

a(1) = 1, a(2) = 2, for n > 2, if n is an odd squarefree number (in A056911), a(n) = 3, otherwise a(n) = running count from 4 onward.