A322588 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A291750(n) for any other number.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 10, 11, 3, 12, 3, 13, 14, 15, 3, 16, 17, 18, 19, 20, 3, 21, 3, 22, 23, 24, 23, 25, 3, 26, 27, 28, 3, 29, 3, 30, 31, 21, 3, 32, 33, 34, 21, 35, 3, 36, 21, 37, 38, 39, 3, 40, 3, 29, 41, 42, 43, 44, 3, 45, 29, 44, 3, 46, 3, 47, 48, 49, 29, 50, 3, 51, 52, 53, 3, 54, 55, 56, 57, 58, 3, 59, 60, 40, 61, 44, 57, 62, 3, 63, 64, 65, 3, 66, 3

Offset: 1

Author

Antti Karttunen, Dec 18 2018

Keywords

• nonn

Comments

For all i, j: a(i) = a(j) => A322318(i) = A322318(j).

Links

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

Crossrefs

Cf. A291750, A291751, A322587, A322589, A322591, A322592.

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; };
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
Aux322588(n) = if((n>2)&&isprime(n),0,(1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n)));
v322588 = rgs_transform(vector(up_to, n, Aux322588(n)));
A322588(n) = v322588[n];