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%I #12 Jan 19 2019 04:15:43
%S 1,2,3,4,5,6,3,7,8,9,3,10,5,6,11,12,5,13,3,14,15,6,3,16,17,9,18,10,5,
%T 19,3,20,15,9,21,22,5,6,11,23,5,24,3,10,25,6,3,26,27,28,11,14,5,29,21,
%U 16,15,9,3,30,5,6,31,32,33,24,3,14,15,34,3,35,5,9,36,10,37,19,3,38,39,9,3,40,33,6,11,16,5,41,42,10,15,6,21,43,5,44,31,45,5,19,3,23,46
%N Let g = A006530(n), the largest prime factor of n. This filter sequence combines (g mod 4), n/g (A052126), and a single bit A319988(n) telling whether the largest prime factor is unitary.
%C Restricted growth sequence transform of triple [A010873(A006530(n)), A052126(n), A319988(n)], with a separate value allotted for a(1).
%C Here among the first 100000 terms, only 2331 have a unique value, compared to 69714 in A320004.
%C For all i, j:
%C a(i) = a(j) => A024362(i) = A024362(j),
%C a(i) = a(j) => A067029(i) = A067029(j),
%C a(i) = a(j) => A071178(i) = A071178(j),
%C a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).
%H Antti Karttunen, <a href="/A319994/b319994.txt">Table of n, a(n) for n = 1..100000</a>
%o (PARI)
%o up_to = 100000;
%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 A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
%o A052126(n) = (n/A006530(n));
%o A319988(n) = ((n>1)&&(factor(n)[omega(n),2]>1));
%o A319994aux(n) = if(1==n,0,[A006530(n)%4, A052126(n), A319988(n)]);
%o v319994 = rgs_transform(vector(up_to,n,A319994aux(n)));
%o A319994(n) = v319994[n];
%Y Cf. A006530, A052126, A319988, A320004.
%Y Cf. also A319996 (modulo 6 analog).
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 05 2018
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