%I #9 Jan 19 2019 04:15:43

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

%T 16,9,5,9,17,3,5,9,12,3,15,3,8,18,5,3,19,20,21,9,8,3,22,9,12,9,5,3,23,

%U 3,5,18,24,9,15,3,8,9,15,3,25,3,5,26,8,9,15,3,19,27,5,3,23,9,5,9,12,3,28,9,8,9,5,9,29,3,30,18,31,3,15,3,12,32

%N Filter sequence combining A000035(n) (parity of n), A003557(n), and A046523(n) (prime signature of n).

%C Restricted growth sequence transform of triple [A000035(n), A003557(n), A046523(n)], or equally, of triple [A007814(n), A003557(n), A046523(n)], or equally, of ordered pair [A000035(n), A291757(n)].

%C For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j).

%H Antti Karttunen, <a href="/A319347/b319347.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 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p=0); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };

%o v319347 = rgs_transform(vector(up_to,n,[A003557(n),(n%2),A046523(n)]));

%o A319347(n) = v319347[n];

%Y Cf. A000035, A003557, A007814, A046523, A291757, A305801, A305891.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 24 2018