%I #7 Jan 25 2024 23:19:15

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

%T 3,22,3,23,12,24,25,26,3,27,28,29,3,30,3,31,32,33,3,34,35,36,37,38,3,

%U 39,28,40,41,42,3,43,3,44,45,46,47,48,3,49,50,51,3,52,3,31,53,54,55,56,3,57,58,59,3,60,61,62,63,64,3,65,37,66

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A342671(i) = A342671(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A001065(n), A342671(n)].

%H Antti Karttunen, <a href="/A369447/b369447.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>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</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 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o Aux369447(n) = [sigma(n)-n, gcd(sigma(n), A003961(n))];

%o v369447 = rgs_transform(vector(up_to, n, Aux369447(n)));

%o A369447(n) = v369447[n];

%Y Cf. A000203, A001065, A003961, A342671.

%Y Cf. also A305801, A369260.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 25 2024