A329608 - OEIS

%I #5 Nov 18 2019 16:42:19

%S 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,

%T 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,

%U 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

%N 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.

%C For all i, j:

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

%H Antti Karttunen, <a href="/A329608/b329608.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%o (PARI)

%o up_to = 100000;

%o 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; };

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

%o A329605(n) = numdiv(A108951(n));

%o Aux329608(n) = if((n%2)&&isprime(n),0,A329605(n));

%o v329608 = rgs_transform(vector(up_to, n, Aux329608(n)));

%o A329608(n) = v329608[n];

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 18 2019