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Ordinal transform of A302043.
2

%I #6 Dec 30 2018 00:05:23

%S 1,1,1,2,1,1,1,2,2,1,1,3,1,1,2,1,1,1,1,3,2,1,1,3,1,1,2,1,1,1,1,2,2,1,

%T 2,3,1,1,3,3,1,1,1,2,1,1,1,2,2,1,1,2,1,1,2,4,3,1,1,4,1,1,1,1,1,1,1,1,

%U 2,1,1,3,1,1,2,1,2,1,1,2,3,1,1,4,2,1,2,1,1,1,5,2,1,1,2,2,1,1,1,3,1,1,1,3,2

%N Ordinal transform of A302043.

%H Antti Karttunen, <a href="/A322870/b322870.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 1024;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

%o v078898 = ordinal_transform(vector(up_to,n,A020639(n)));

%o A078898(n) = v078898[n];

%o A302042(n) = if((1==n)||isprime(n),1,my(c = A078898(n), p = prime(-1+primepi(A020639(n))+primepi(A020639(c))), d = A078898(c), k=0); while(d, k++; if((1==k)||(A020639(k)>=p),d -= 1)); (k*p));

%o A302043(n) = (n - A302042(n));

%o v322870 = ordinal_transform(vector(up_to,n,A302043(n)));

%o A322870(n) = v322870[n];

%Y Cf. A078898, A302042, A302043, A322871.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 29 2018