A323081 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(p) = -(p mod 4) for primes p, and f(n) = A252463(n) for any other numbers.

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

Offset: 1

Author

Antti Karttunen, Jan 03 2019

Keywords

• nonn

Comments

For all i, j:

A319704(i) = A319704(j) => a(i) = a(j) => A322805(i) = A322805(j).

Links

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

Crossrefs

Cf. A292583, A319704, A322805, A323080.

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A323081aux(n) = if(isprime(n),-(n%4),A252463(n));
v323081 = rgs_transform(vector(up_to,n,A323081aux(n)));
A323081(n) = v323081[n];