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%I #10 Apr 05 2018 20:33:42
%S 1,2,2,3,2,4,2,5,3,4,2,6,2,4,4,7,2,6,2,6,5,4,2,8,3,4,4,6,2,9,2,10,6,4,
%T 4,11,2,4,4,8,2,8,2,6,7,4,2,12,3,6,6,6,2,9,5,8,6,4,2,13,2,4,4,14,4,13,
%U 2,6,8,9,2,15,2,4,4,6,4,9,2,12,6,4,2,15,6,4,9,8,2,12,5,6,10,4,4,16,2,6,4,11,2,13,2,8,11
%N A filter sequence analogous to A101296 for nonstandard factorization based on the sieve of Eratosthenes (A083221).
%C Restricted growth sequence transform of A278524.
%C See A302042 for the description of the nonstandard factorization employed here.
%C For all i, j:
%C a(i) = a(j) => A253557(i) = A253557(j).
%C a(i) = a(j) => A302041(i) = A302041(j).
%C a(i) = a(j) => A302050(i) = A302050(j).
%C a(i) = a(j) => A302051(i) = A302051(j) => A302052(i) = A302052(j).
%H Antti Karttunen, <a href="/A302046/b302046.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%o (PARI)
%o up_to = 32769;
%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 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A020639(n) = { if(1==n,n,vecmin(factor(n)[, 1])); };
%o A078898(n) = { if(n<=1,n, my(spf=A020639(n),k=1,m=n/spf); while(m>1,if(A020639(m)>=spf,k++); m--); (k)); };
%o A001511(n) = 1+valuation(n,2);
%o A302045(n) = A001511(A078898(n));
%o A302044(n) = if(1==n,n,my(k=0); while((n%2), n = A268674(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A250469(n); k--); (n));
%o A302041(n) = if(1==n, 0,1+A302041(A302044(n)));
%o Aux302046(n) = if(1==n,n, my(k=A302041(n), v = vector(k),i=1); while(n>1,v[i] = A302045(n); n = A302044(n); i++); vecsort(v));
%o write_to_bfile(1,rgs_transform(vector(up_to,n,Aux302046(n))),"b302046.txt");
%Y Cf. A101296, A250246, A278524, A302042, A302044, A302045.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 31 2018
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