%I #5 Sep 16 2018 21:43:54
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,32,33,34,35,36,37,38,35,39,40,41,42,43,44,45,46,47,48,
%U 49,50,44,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,68,76,77,78,79,80,81,82,83,84,85,86,87,88,89,75,90
%N Filter sequence combining the prime signature of n (A046523) with A289625.
%C Restricted growth sequence transform of A289628.
%C For all i, j: a(i) = a(j) => A318893(i) = A318893(j).
%H Antti Karttunen, <a href="/A318892/b318892.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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
%o A318892aux(n) = [A046523(n), A289625(n)];
%o v318892 = rgs_transform(vector(up_to,n,A318892aux(n)));
%o A318892(n) = v318892[n];
%Y Cf. A046523, A289625, A289628, A318839, A318893.
%K nonn
%O 1,2
%A _Antti Karttunen_, Sep 16 2018