%I #5 Feb 22 2020 18:02:20

%S 1,2,3,4,5,6,7,4,8,9,10,11,12,13,13,4,14,15,16,17,18,19,20,21,22,23,

%T 24,25,26,27,28,4,29,30,29,31,32,33,34,35,36,37,38,39,40,41,42,43,44,

%U 45,41,46,47,48,41,49,50,51,52,53,54,55,56,4,57,58,59,60,55,58,61,62,63,64,65,66,55,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,76

%N Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003557(n), A046523(n), A048250(n)] for all other numbers, except f(2^k) = 0 for k >= 2.

%C For all i, j:

%C A295300(i) = A295300(j) => a(i) = a(j),

%C a(i) = a(j) => A048250(i) = A048250(j),

%C a(i) = a(j) => A332455(i) = A332455(j),

%C a(i) = a(j) => A332459(i) = A332459(j).

%H Antti Karttunen, <a href="/A332230/b332230.txt">Table of n, a(n) for n = 1..65537</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 A003557(n) = n/factorback(factor(n)[, 1]); \\ From A003557

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

%o A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

%o A209229(n) = (n && !bitand(n,n-1));

%o A291750(n) = (1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n));

%o Aux332230(n) = if((n>2)&&A209229(n),0,(1/2)*(2 + ((A046523(n) + A291750(n))^2) - A046523(n) - 3*A291750(n)));

%o v332230 = rgs_transform(vector(up_to,n,Aux332230(n)));

%o A332230(n) = v332230[n];

%Y Cf. A003557, A046523, A048250, A295300, A332455, A332459.

%Y Cf. also A326199.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 22 2020