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%I #9 Nov 08 2018 21:13:33
%S 1,2,3,4,5,6,7,4,8,9,10,11,12,13,14,4,15,16,17,18,12,19,20,11,21,22,
%T 23,24,25,26,27,4,28,29,30,11,31,32,30,18,33,22,34,35,36,37,38,11,39,
%U 40,41,42,43,44,33,24,31,45,46,47,48,49,50,4,51,52,53,54,55,56,57,11,58,59,60,61,48,56,62,18,63,64,65,42,66,67,68,35,69,70,58,71,48,72,58,11,73,74,75,18,76,77,78,42
%N Filter sequence combining A173557(n) with A319993(n).
%C Restricted growth sequence transform of ordered pair [A173557(n), A319993(n)].
%C For all i, j: a(i) = a(j) => A319997(i) = A319997(j).
%H Antti Karttunen, <a href="/A319999/b319999.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 A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
%o A319993(n) = { my(f=factor(n)); prod(i=1,#f~,if(2==f[i,1],-(1==f[i,2]),(f[i,1]^(f[i,2]-1)))); };
%o v319999 = rgs_transform(vector(up_to,n,[A173557(n),A319993(n)]));
%o A319999(n) = v319999[n];
%Y Cf. A173557, A319993, A319997.
%Y Cf. also A295886, A295887.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 08 2018
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