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%I #7 Jul 17 2020 22:58:33
%S 1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,3,1,3,1,2,1,2,1,3,2,2,1,2,1,3,1,4,1,2,
%T 2,2,1,2,1,3,1,3,1,2,1,2,1,4,1,2,1,2,1,4,2,3,1,2,1,2,1,2,1,4,2,3,1,2,
%U 1,2,1,3,1,2,2,2,1,3,1,4,1,2,1,2,2,2,1,3,1,4,1,2,1,2,2,4,1,3,1,3,1,3,1,3,2
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336120(i)) = A278222(A336120(j)) for all i, j >= 1.
%C Restricted growth sequence transform of A278222(A336120(n)).
%C For all i, j:
%C a(i) = a(j) => A336121(i) = A336121(j) => A335909(i) = A335909(j).
%H Antti Karttunen, <a href="/A336312/b336312.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 1024; \\ 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 \\ Needs also code from A336124:
%o A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
%o A336120(n) = if(1==n,0,(3==A336124(n))+(2*A336120(A253553(n))));
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A278222(n) = A046523(A005940(1+n));
%o v336312 = rgs_transform(vector(up_to,n,A278222(A336120(n))));
%o A336312(n) = v336312[n];
%Y Cf. A336311, A336313.
%Y Cf. A336119 (positions of ones).
%Y Cf. also A292583, A332901, A335909, A336121.
%K nonn
%O 1,4
%A _Antti Karttunen_, Jul 17 2020
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