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A380460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A380459(i) = A380459(j), for all i, j >= 1, where A380459(n) = Product_{d|n} A276086(d)^A349394(n/d).

%I A380460 #10 Feb 03 2025 11:55:01
%S A380460 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A380460 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A380460 8,40,41,21,2,42,2,43,44,45,46,47,2,48,49,50,2,51,2,52,53,54,46,55,2,56,57,58,2,59,60,61,20,62,2,63,64,65,66,67,68,69,2,70,71
%N A380460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A380459(i) = A380459(j), for all i, j >= 1, where A380459(n) = Product_{d|n} A276086(d)^A349394(n/d).
%C A380460 Restricted growth sequence transform of A380459.
%C A380460 For all i, j >= 1:
%C A380460   A305800(i) = A305800(j) => a(i) = a(j),
%C A380460   a(i) = a(j) => A003415(i) = A003415(j),
%C A380460   a(i) = a(j) => A380467(i) = A380467(j),
%C A380460   a(i) = a(j) => A380477(i) = A380477(j).
%H A380460 Antti Karttunen, <a href="/A380460/b380460.txt">Table of n, a(n) for n = 1..100000</a>
%o A380460 (PARI)
%o A380460 up_to = 100000;
%o A380460 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 A380460 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A380460 A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
%o A380460 A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
%o A380460 v380460 = rgs_transform(vector(up_to, n, A380459(n)));
%o A380460 A380460(n) = v380460[n];
%Y A380460 Cf. A276086, A349394, A380459.
%Y A380460 Cf. A003415, A305800, A380467, A380477.
%Y A380460 Cf. also A329351, A329381.
%K A380460 nonn
%O A380460 1,2
%A A380460 _Antti Karttunen_, Jan 31 2025