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%I #10 May 24 2024 16:32:54
%S 1,2,1,1,1,3,1,2,1,4,1,5,1,4,6,1,1,7,1,8,1,4,1,9,1,4,10,11,1,12,1,13,
%T 14,4,15,16,1,4,1,17,1,3,1,18,6,4,1,5,1,2,14,19,1,20,1,21,10,4,1,22,1,
%U 4,1,1,23,3,1,24,14,25,1,26,1,4,27,28,29,3,1,4,1,4,1,30,1,4,31,32,1,33,34,18,1,4,35,36,1,2,37,23
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A322361(i) = A322361(j) and A342671(i) = A342671(j), for all i, j >= 1.
%C Restricted growth sequence transform of the triple [A009194(n), A322361(n), A342671(n)].
%C For all i, j:
%C a(i) = a(j) => A349167(i) = A349167(j),
%C a(i) = a(j) => A353666(i) = A353666(j),
%C a(i) = a(j) => A372565(i) = A372565(j).
%H Antti Karttunen, <a href="/A372572/b372572.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 Aux372572(n) = [gcd(n, sigma(n)), gcd(n, A003961(n)), gcd(sigma(n), A003961(n))];
%o v372572 = rgs_transform(vector(up_to, n, Aux372572(n)));
%o A372572(n) = v372572[n];
%Y Cf. A009194, A322361, A342671, A349167, A353666, A372565.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 24 2024
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