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A318893 Filter sequence combining the prime signature of n (A046523) with Euler totient function (A000010).

%I A318893 #6 Sep 16 2018 21:44:01
%S A318893 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,21,
%T A318893 26,27,28,29,30,31,32,33,34,35,36,37,34,38,39,40,41,42,43,44,45,46,47,
%U A318893 42,48,43,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,53,70,59,71,66,72,73,74,51,75,76,77,78,79,80,81,76,82,83,71
%N A318893 Filter sequence combining the prime signature of n (A046523) with Euler totient function (A000010).
%C A318893 Restricted growth sequence transform of A286160.
%C A318893 For all i, j: a(i) = a(j) => A062355(i) = A062355(j).
%H A318893 Antti Karttunen, <a href="/A318893/b318893.txt">Table of n, a(n) for n = 1..65537</a>
%o A318893 (PARI)
%o A318893 up_to = 65537;
%o A318893 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 A318893 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A318893 A318893aux(n) = [eulerphi(n), A046523(n)];
%o A318893 v318893 = rgs_transform(vector(up_to,n,A318893aux(n)));
%o A318893 A318893(n) = v318893[n];
%Y A318893 Cf. A000010, A046523, A286160, A318839, A318892.
%Y A318893 Cf. also A061468, A062355.
%K A318893 nonn
%O A318893 1,2
%A A318893 _Antti Karttunen_, Sep 16 2018