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A372570 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)], for all i, j >= 1.

%I A372570 #6 May 25 2024 17:00:00
%S A372570 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,8,3,16,17,10,18,19,3,
%T A372570 20,3,21,22,8,23,24,3,10,25,26,3,27,3,28,29,8,3,30,31,32,33,34,3,35,
%U A372570 36,37,38,8,3,39,3,10,40,41,42,43,3,44,22,45,3,46,3,10,47,48,49,50,3,51,52,8,3,53,54,10,55,56,3,57,58,28,15,8,59,60,3,61,62,63,3
%N A372570 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)], for all i, j >= 1.
%C A372570 Restricted growth sequence transform of the quintuple [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)].
%C A372570 For all i, j:
%C A372570   A305801(i) = A305801(j) => a(i) = a(j),
%C A372570   a(i) = a(j) => A372569(i) = A372569(j),
%C A372570   a(i) = a(j) => A372572(i) = A372572(j).
%H A372570 Antti Karttunen, <a href="/A372570/b372570.txt">Table of n, a(n) for n = 1..65537</a>
%o A372570 (PARI)
%o A372570 up_to = 65537;
%o A372570 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 A372570 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A372570 Aux372570(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n)), gcd(n, A003961(n)), gcd(sigma(n), A003961(n))];
%o A372570 v372570 = rgs_transform(vector(up_to, n, Aux372570(n)));
%o A372570 A372570(n) = v372570[n];
%Y A372570 Cf. A009194, A009195, A009223, A322361, A342671.
%Y A372570 Cf. also A305801, A372569, A372572.
%K A372570 nonn
%O A372570 1,2
%A A372570 _Antti Karttunen_, May 25 2024