A328471 - OEIS

%I #7 Oct 18 2019 21:28:19

%S 1,1,2,1,2,3,3,1,2,4,5,5,2,2,5,1,2,5,5,6,5,2,5,7,2,3,8,2,5,9,5,1,2,6,

%T 9,5,5,5,5,10,2,2,10,5,2,5,11,9,2,5,9,2,9,11,9,5,2,12,10,10,2,2,5,1,5,

%U 13,12,5,9,5,14,10,5,2,10,2,5,5,12,15,2,2,10,3,10,12,9,2,2,16,5,12,10,2,5,5,2,5,5,9,5,5,10,5,2

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328461(i)) = A046523(A328461(j)) for all i, j.

%C Restricted growth sequence transform of function f(n) = A046523(A276156(n)/A002110(A007814(n))).

%H Antti Karttunen, <a href="/A328471/b328471.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</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 A002110(n) = prod(i=1,n,prime(i));

%o A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };

%o A328461(n) = (A276156(n)/A002110(valuation(n,2)));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o v328471 = rgs_transform(vector(up_to, n, A046523(A328461(n))));

%o A328471(n) = v328471[n];

%Y Cf. A002110, A007814, A046523, A276156, A328461, A328472, A328474.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 18 2019