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A369259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.

%I A369259 #9 Jan 25 2024 15:29:00
%S A369259 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,15,23,24,25,
%T A369259 26,27,28,29,21,30,31,32,31,33,34,35,36,37,38,39,40,41,42,29,31,43,44,
%U A369259 45,46,47,48,49,46,50,51,52,53,54,55,39,56,57,58,59,60,61,62,59,46,63,64,65,66,67,62,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,59
%N A369259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j), A048250(i) = A048250(j) and A342671(i) = A342671(j), for all i, j >= 1.
%C A369259 Restricted growth sequence transform of the triplet [A003557(j), A048250(i), A342671(n)].
%C A369259 For all i, j >= 1:
%C A369259   a(i) = a(j) => A323368(i) = A323368(j) => A291751(i) = A291751(j),
%C A369259   a(i) = a(j) => A369260(i) = A369260(j) => A286603(i) = A286603(j).
%H A369259 Antti Karttunen, <a href="/A369259/b369259.txt">Table of n, a(n) for n = 1..65537</a>
%H A369259 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A369259 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A369259 (PARI)
%o A369259 up_to = 65537;
%o A369259 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 A369259 A003557(n) = (n/factorback(factor(n)[, 1]));
%o A369259 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A369259 A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
%o A369259 A342671(n) = gcd(sigma(n), A003961(n));
%o A369259 Aux369259(n) = [A003557(n), A048250(n), A342671(n)];
%o A369259 v369259 = rgs_transform(vector(up_to, n, Aux369259(n)));
%o A369259 A369259(n) = v369259[n];
%Y A369259 Cf. A000203, A001615, A003557, A003961, A048250, A286603, A291751, A369260.
%Y A369259 Differs from related A296089 and A323368 for the first time at n=79, where a(79) = 69, while A296089(79) = A323368(79) = 51.
%K A369259 nonn
%O A369259 1,2
%A A369259 _Antti Karttunen_, Jan 25 2024