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A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.

%I A379002 #6 Dec 15 2024 12:12:00
%S A379002 1,2,2,3,4,5,2,6,3,7,2,8,2,5,7,9,2,8,2,10,5,5,2,11,12,5,6,8,2,13,2,14,
%T A379002 5,5,7,15,2,5,5,16,2,17,2,8,10,5,2,18,3,19,5,8,2,11,7,11,5,5,2,20,2,5,
%U A379002 8,21,7,17,2,8,5,13,2,22,2,5,19,8,5,17,2,23,9,5,2,24,7,5,5,11,2,20,5,8,5,5,7,25,2,8,8,26,2,17,2,11,13
%N A379002 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A112765(i) = A112765(j), for all i, j, where A046523 gives the least representative of the prime signature of n and A112765 gives the 5-adic valuation of n.
%C A379002 Restricted growth sequence transform of ordered pair [A046523(n), A112765(n)].
%C A379002 For all i, j:
%C A379002   A379001(i) = A379001(j) => a(i) = a(j).
%H A379002 Antti Karttunen, <a href="/A379002/b379002.txt">Table of n, a(n) for n = 1..100000</a>
%o A379002 (PARI)
%o A379002 up_to = 100000;
%o A379002 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 A379002 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A379002 v379002 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n,5)]));
%o A379002 A379002(n) = v379002[n];
%Y A379002 Cf. A046523, A112765, A379001.
%Y A379002 Cf. also A305891, A305893.
%K A379002 nonn
%O A379002 1,2
%A A379002 _Antti Karttunen_, Dec 15 2024