A329608 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A329605(n) for all other n, except for odd primes p, f(p) = 0.

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

Offset: 1

Author

Antti Karttunen, Nov 18 2019

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j) => A329614(i) = A329614(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000005, A108951, A305801, A329605, A329606, A329614.

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; };
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A329605(n) = numdiv(A108951(n));
Aux329608(n) = if((n%2)&&isprime(n),0,A329605(n));
v329608 = rgs_transform(vector(up_to, n, Aux329608(n)));
A329608(n) = v329608[n];