cp's OEIS Frontend

A351034 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351032(i) = A351032(j), for all i, j >= 1.

%I A351034 #8 Jan 29 2022 22:31:44
%S A351034 1,1,1,2,1,2,1,3,1,2,1,4,1,5,1,6,1,7,1,6,8,5,1,9,1,2,1,10,1,11,1,12,8,
%T A351034 2,8,9,1,2,1,13,1,14,1,11,15,5,1,16,8,17,1,11,1,18,8,19,1,5,1,20,1,21,
%U A351034 8,13,1,22,1,6,8,10,1,23,1,21,24,4,25,22,1,26,27,21,1,28,1,29,8,30,1,31,8,10,15,2,1
%N A351034 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351032(i) = A351032(j), for all i, j >= 1.
%C A351034 Restricted growth sequence transform of A351032.
%H A351034 Antti Karttunen, <a href="/A351034/b351034.txt">Table of n, a(n) for n = 1..65537</a>
%H A351034 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A351034 (PARI)
%o A351034 up_to = 65537;
%o A351034 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 A351034 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351034 A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
%o A351034 A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
%o A351034 A291759(n) = A289814(A048673(n));
%o A351034 A351032(n) = { my(m=1); fordiv(n,d,if(d<n,m *= A019565(A291759(d)))); (m); };
%o A351034 v351034 = rgs_transform(vector(up_to, n, A351032(n)));
%o A351034 A351034(n) = v351034[n];
%Y A351034 Cf. A019565, A048673, A289814, A291759, A351030, A351032, A351033.
%Y A351034 Cf. also A293224.
%K A351034 nonn
%O A351034 1,4
%A A351034 _Antti Karttunen_, Jan 29 2022