A373595 - OEIS

%I #12 Jun 13 2024 10:51:04

%S 1,2,3,4,5,6,5,7,8,4,5,9,5,10,6,11,5,12,5,7,13,4,5,14,4,10,15,16,5,9,

%T 5,17,6,4,10,18,5,10,13,11,5,19,5,7,12,4,5,20,21,7,6,16,5,22,4,23,13,

%U 4,5,14,5,10,24,25,10,9,5,7,6,16,5,26,5,10,9,16,10,19,5,17,27,4,5,28,4,10,6,11,5,18,21,7,13,4,10,29,5,30,12,11,5,9,5,23,19

%N Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A373591(n), A373592(n)].

%C Restricted growth sequence transform of the function f given in the definition.

%C For all i, j > 1:

%C   A305900(i) = A305900(j) => A373594(i) = A373594(j) => a(i) = a(j),

%C   A373593(i) = A373593(j) => a(i) = a(j),

%C   a(i) = a(j) => b(i) = b(j), where b can be (but is not limited to) any of the sequences listed at the crossrefs-section, under "some of the matched sequences".

%H Antti Karttunen, <a href="/A373595/b373595.txt">Table of n, a(n) for n = 1..100000</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 A007949(n) = valuation(n,3);

%o A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]);

%o A373592(n) = sum(i=1, #n=factor(n)~, (2==n[1, i]%3)*n[2, i]);

%o Aux373595(n) = if(n<=3, n, if(isprime(n), 0, [A007949(n), A373591(n), A373592(n)]));

%o v373595 = rgs_transform(vector(up_to, n, Aux373595(n)));

%o A373595(n) = v373595[n];

%Y Cf. A007949, A373591, A373592.

%Y Cf. A305900, A373593, A373594.

%Y Some of the matched sequences (see comments): A001222, A359430, A369643, A369658, A373371, A373383, A373474, A373491, A373493, A373585, A373588, A373596.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 13 2024