A324203 - OEIS

%I #7 Feb 19 2019 18:20:49

%S 1,2,2,3,2,4,2,5,3,4,2,6,2,4,4,7,2,8,2,9,4,4,2,10,3,4,5,9,2,11,2,12,4,

%T 4,4,13,2,4,4,14,2,11,2,9,6,4,2,15,3,8,4,9,2,16,4,17,4,4,2,18,2,4,9,

%U 19,4,11,2,9,4,11,2,20,2,4,8,9,4,11,2,21,7,4,2,20,4,4,4,17,2,22,4,9,4,4,4,23,2,8,9,24,2,11,2,17,11

%N Lexicographically earliest sequence such that a(i) = a(j) => A324202(i) = A324202(j) for all i, j >= 1.

%C Restricted growth sequence transform of A324202.

%C For all i, j:

%C   a(i) = a(j) => A324190(i) = A324190(j),

%C   a(i) = a(j) => A324191(i) = A324191(j).

%H Antti Karttunen, <a href="/A324203/b324203.txt">Table of n, a(n) for n = 1..65537</a>

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

%o (PARI)

%o up_to = 65537;

%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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));

%o A324202(n) = A046523(factorback(apply(x -> prime(1+x),apply(A297167, select(d -> d>1,divisors(n))))));

%o v324203 = rgs_transform(vector(up_to, n, A324202(n)));

%o A324203(n) = v324203[n];

%Y Cf. A300827, A324181, A324190, A324191, A324202.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 19 2019