A369260 - OEIS

%I #10 Jan 25 2024 15:29:05

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,15,23,16,24,

%T 25,26,27,28,21,29,30,31,30,32,33,34,26,35,36,37,38,39,40,28,30,41,42,

%U 43,44,45,46,47,44,48,49,50,51,52,53,37,54,55,56,57,58,59,60,57,44,61,62,63,41,64,60,65,66,67,68,69,70,71,72,73,74,75,76,77,78,65,79,57

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A342671(i) = A342671(j) and A349162(i) = A349162(j), for all i, j >=  1.

%C Restricted growth sequence transform of the ordered pair [A342671(n), A349162(n)], or equally, of the pair [A000203(n), A342671(n)], or equally, of the pair [A000203(n), A349162(n)].

%C For all i, j >= 1:

%C   A369259(i) = A369259(j) => a(i) = a(j) => A286603(i) = A286603(j).

%H Antti Karttunen, <a href="/A369260/b369260.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 A342671(n) = gcd(sigma(n), A003961(n));

%o Aux369260(n) = { my(u=A342671(n)); [u, sigma(n)/u]; };

%o v369260 = rgs_transform(vector(up_to, n, Aux369260(n)));

%o A369260(n) = v369260[n];

%Y Cf. A000203, A003961, A342671, A348993, A349162.

%Y Cf. also A286603, A291751, A369259, A369261.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 25 2024