cp's OEIS Frontend

A318891 Filter sequence combining the prime signature of n (A046523) with the largest prime factor of n (A006530).

%I A318891 #7 Sep 16 2018 21:43:47
%S A318891 1,2,3,4,5,6,7,8,9,10,11,12,13,14,10,15,16,12,17,18,14,19,20,21,22,23,
%T A318891 24,25,26,27,28,29,19,30,14,31,32,33,23,34,35,36,37,38,18,39,40,41,42,
%U A318891 18,30,43,44,21,19,45,33,46,47,48,49,50,25,51,23,52,53,54,39,36,55,56,57,58,18,59,19,60,61,62,63,64,65,66,30,67,46,68,69,48,23,70,50
%N A318891 Filter sequence combining the prime signature of n (A046523) with the largest prime factor of n (A006530).
%C A318891 Restricted growth sequence transform of A286356.
%C A318891 For all i, j: a(i) = a(j) => A297112(i) = A297112(j). (Also, equivalently, A297113 or A297167 in place of A297112.)
%H A318891 Antti Karttunen, <a href="/A318891/b318891.txt">Table of n, a(n) for n = 1..65537</a>
%o A318891 (PARI)
%o A318891 up_to = 65537;
%o A318891 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 A318891 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A318891 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o A318891 A318891aux(n) = [A046523(n), A061395(n)];
%o A318891 v318891 = rgs_transform(vector(up_to,n,A318891aux(n)));
%o A318891 A318891(n) = v318891[n];
%Y A318891 Cf. A006530, A046523, A061395, A286356, A318890.
%Y A318891 Cf. also A297112, A297113, A297167.
%K A318891 nonn
%O A318891 1,2
%A A318891 _Antti Karttunen_, Sep 16 2018