cp's OEIS Frontend

A336161 Lexicographically earliest infinite sequence such that a(i) = a(j) => A087436(i) = A087436(j) and A335915(i) = A335915(j) for all i, j >= 1.

%I A336161 #5 Jul 10 2020 22:07:17
%S A336161 1,1,2,1,3,2,3,1,4,3,5,2,6,3,7,1,8,4,9,3,7,5,10,2,11,6,12,3,13,7,5,1,
%T A336161 14,8,11,4,15,9,16,3,13,7,17,5,18,10,19,2,11,11,11,6,20,12,21,3,21,13,
%U A336161 22,7,23,5,18,1,24,14,25,8,26,11,27,4,28,15,29,9,21,16,30,3,31,13,32,7,33,17,34,5,35,18,24,10,14,19,36,2,37,11,38,11,39,11,40,6,29
%N A336161 Lexicographically earliest infinite sequence such that a(i) = a(j) => A087436(i) = A087436(j) and A335915(i) = A335915(j) for all i, j >= 1.
%C A336161 Restricted growth sequence transform of the ordered pair [A087436(n), A335915(n)].
%C A336161 For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A335904(i) = A335904(j).
%H A336161 Antti Karttunen, <a href="/A336161/b336161.txt">Table of n, a(n) for n = 1..65537</a>
%o A336161 (PARI)
%o A336161 up_to = 65537;
%o A336161 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 A336161 A087436(n) = (bigomega(n>>valuation(n,2)));
%o A336161 A000265(n) = (n>>valuation(n,2));
%o A336161 A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
%o A336161 Aux336161(n) = [A087436(n),A335915(n)];
%o A336161 v336161 = rgs_transform(vector(up_to, n, Aux336161(n)));
%o A336161 A336161(n) = v336161[n];
%Y A336161 Cf. A087436, A335915.
%Y A336161 Cf. also A324400, A335880, A335904.
%K A336161 nonn
%O A336161 1,3
%A A336161 _Antti Karttunen_, Jul 10 2020