cp's OEIS Frontend

A336471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336471 #28 Jul 25 2020 10:36:10
%S A336471 1,1,2,1,2,2,3,1,4,2,3,2,3,3,5,1,2,4,6,2,7,3,6,2,4,3,8,3,6,5,6,1,7,2,
%T A336471 7,4,6,6,7,2,3,7,9,3,10,6,9,2,11,4,5,3,6,8,7,3,12,6,9,5,6,6,13,1,7,7,
%U A336471 9,2,12,7,9,4,6,6,10,6,12,7,9,2,14,3,6,7,5,9,12,3,6,10,12,6,12,9,12,2,3,11,13,4,6,5,6,3,15
%N A336471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336471 Restricted growth sequence transform of the ordered pair [A329697(n), A336158(n)].
%C A336471 For all i, j:
%C A336471   A336470(i) = A336470(j) => a(i) = a(j)
%C A336471   a(i) = a(j) => A336396(i) = A336396(j),
%C A336471   a(i) = a(j) => A336469(i) = A336469(j) => A336477(i) = A336477(j).
%C A336471 This sequence has an ability to see where the terms of A003401 are, as they are the indices of zeros in A336469. Specifically, they are numbers k that satisfy the condition A329697(k) = A001221(A336158(k)), i.e., numbers for which A329697(k) is equal to the number of distinct prime divisors of the odd part of k. See also comments in array A334100.
%H A336471 Antti Karttunen, <a href="/A336471/b336471.txt">Table of n, a(n) for n = 1..65537</a>
%o A336471 (PARI)
%o A336471 up_to = 65537;
%o A336471 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 A336471 A000265(n) = (n>>valuation(n,2));
%o A336471 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336471 A336158(n) = A046523(A000265(n));
%o A336471 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A336471 Aux336471(n) = [A329697(n), A336158(n)];
%o A336471 v336471 = rgs_transform(vector(up_to, n, Aux336471(n)));
%o A336471 A336471(n) = v336471[n];
%Y A336471 Cf. A000265, A003401, A046523, A329697, A334100, A336158.
%Y A336471 Cf. also A003602, A324400, A336159, A336160, A336396, A336469, A336470, A336472, A336473, A336477.
%K A336471 nonn
%O A336471 1,3
%A A336471 _Antti Karttunen_, Jul 22 2020