A365466 - OEIS

%I #9 Sep 04 2023 18:23:44

%S 1,1,1,1,1,1,2,1,1,1,3,1,2,2,4,1,1,1,5,1,2,3,6,1,1,2,4,2,7,4,8,1,3,1,

%T 2,1,5,5,9,1,3,2,10,3,11,6,12,1,5,1,4,2,13,4,14,2,15,7,16,4,8,8,17,1,

%U 2,3,18,1,19,2,20,1,5,5,21,5,22,9,23,1,1,3,24,2,11,10,25,3,6,11,26,6,27,12,28,1,2,5

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336466(A163511(i)) = A336466(A163511(j)) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p.

%C Restricted growth sequence transform of the ordered pair [A336466(n), A365426(n)].

%C For all i, j: A003602(i) = A003602(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A365466/b365466.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 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 A000265(n) = (n>>valuation(n,2));

%o A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };

%o A365466aux(n) = [A336466(n), A336466(A163511(n))];

%o v365466 = rgs_transform(vector(up_to,n,A365466aux(n)));

%o A365466(n) = v365466[n];

%Y Cf. A000265, A003602, A163511, A336466, A365426.

%Y Cf. also A365467.

%K nonn

%O 1,7

%A _Antti Karttunen_, Sep 04 2023