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A331747 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A278222(i) = A278222(j) for all i, j.

%I A331747 #8 Feb 04 2020 21:44:50
%S A331747 1,1,2,1,3,4,5,1,3,6,7,8,7,9,10,1,3,11,7,6,12,13,14,15,7,13,16,17,14,
%T A331747 18,19,1,11,6,7,3,12,13,14,20,12,21,22,23,24,25,26,8,7,7,27,13,22,28,
%U A331747 29,30,14,25,29,31,26,32,33,1,3,34,7,6,35,13,14,11,12,36,22,23,22,37,26,6,12,36,22,38,39,40,41,23,22,42,43,44,45,46,47,15,7,7,27,7
%N A331747 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A278222(i) = A278222(j) for all i, j.
%C A331747 Restricted growth sequence transform of the ordered pair [A009194(n), A278222(n)].
%C A331747 For all i, j:
%C A331747    A331746(i) = A331746(j) => a(i) = a(j).
%H A331747 Antti Karttunen, <a href="/A331747/b331747.txt">Table of n, a(n) for n = 1..65537</a>
%H A331747 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A331747 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A331747 a(2^n) = 1 for all n >= 0.
%o A331747 (PARI)
%o A331747 up_to = 65537;
%o A331747 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 A331747 A009194(n) = gcd(n, sigma(n));
%o A331747 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1)));
%o A331747 t };
%o A331747 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A331747 A278222(n) = A046523(A005940(1+n));
%o A331747 Aux331747(n) = [A009194(n),A278222(n)];
%o A331747 v331747 = rgs_transform(vector(up_to, n, Aux331747(n)));
%o A331747 A331747(n) = v331747[n];
%Y A331747 Cf. A009194, A278222.
%Y A331747 Cf. also A324400, A286622, A318310, A318311, A324389, A331744, A331745, A331746.
%K A331747 nonn
%O A331747 1,3
%A A331747 _Antti Karttunen_, Feb 04 2020