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A379001 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.

%I A379001 #7 Dec 15 2024 12:12:04
%S A379001 1,2,3,4,5,6,7,8,9,10,7,11,7,12,13,14,7,15,7,16,17,12,7,18,19,12,20,
%T A379001 21,7,22,7,23,17,12,24,25,7,12,17,26,7,27,7,21,28,12,7,29,30,31,17,21,
%U A379001 7,32,24,33,17,12,7,34,7,12,35,36,24,27,7,21,17,37,7,38,7,12,39,21,40,27,7,41,42,12,7,43,24,12,17,33,7,44,40,21,17,12,24,45,7,46,35
%N A379001 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), v_2(i) = v_2(j), v_3(i) = v_3(j) and v_5(i) = v_5(j), for all i, j, where v_2 (A007814), v_3 (A007949) and v_5 (A112765) give the 2-, 3- and 5-adic valuations of n respectively.
%C A379001 Restricted growth sequence transform of ordered 4-tuple [A046523(n), A007814(n), A007949(n), A112765(n)].
%C A379001 For all i, j:
%C A379001   A379000(i) = A379000(j) => a(i) = a(j),
%C A379001   a(i) = a(j) => A358230(i) = A358230(j),
%C A379001   a(i) = a(j) => A379002(i) = A379002(j),
%C A379001   a(i) = a(j) => A379005(i) = A379005(j).
%H A379001 Antti Karttunen, <a href="/A379001/b379001.txt">Table of n, a(n) for n = 1..100000</a>
%o A379001 (PARI)
%o A379001 up_to = 100000;
%o A379001 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 A379001 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A379001 v379001 = rgs_transform(vector(up_to, n, [A046523(n), valuation(n,2), valuation(n,3), valuation(n,5)]));
%o A379001 A379001(n) = v379001[n];
%Y A379001 Cf. A046523, A007814, A007949, A112765.
%Y A379001 Cf. A358230, A379000, A379002, A379005.
%K A379001 nonn
%O A379001 1,2
%A A379001 _Antti Karttunen_, Dec 15 2024