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%I #6 Oct 03 2018 21:36:00
%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,4,17,18,19,2,
%T 20,2,21,22,23,18,24,2,25,26,27,2,28,2,29,30,31,2,32,33,34,12,35,2,36,
%U 37,38,39,40,2,41,2,42,43,44,45,46,2,47,48,49,2,50,2,51,52,53,45,54,2,55,56,57,2,58,59,60,61,62,2,63,64,65,66,67,68,69,2,70,71
%N Filter sequence combining primorial base representations of the proper divisors of n; Restricted growth sequence transform of A319708.
%C For all i, j:
%C a(i) = a(j) => A001065(i) = A001065(j),
%C a(i) = a(j) => A319713(i) = A319713(j).
%H Antti Karttunen, <a href="/A319709/b319709.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 A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A319708(n) = { my(m=1); fordiv(n, d, if(d<n, m *= A276086(d))); (m); };
%o v319709 = rgs_transform(vector(up_to,n,A319708(n)));
%o A319709(n) = v319709[n];
%Y Cf. A276086, A319708, A319713.
%Y Cf. A293215, A293226, A300835 for similar constructions for other bases.
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 03 2018
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