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A346486 a(1) = 1; for n > 1, a(n) = A020639(n) * a(A302044(n)).

%I A346486 #11 Apr 27 2022 15:57:59
%S A346486 1,2,3,2,5,6,7,2,3,10,11,6,13,14,15,2,17,6,19,10,3,22,23,6,5,26,21,14,
%T A346486 29,30,31,2,15,34,35,6,37,38,33,10,41,6,43,22,3,46,47,6,7,10,15,26,53,
%U A346486 42,5,14,21,58,59,30,61,62,39,2,55,30,67,34,15,70,71,6,73,74,51,38,77,66,79,10,33,82,83,6,35
%N A346486 a(1) = 1; for n > 1, a(n) = A020639(n) * a(A302044(n)).
%H A346486 Antti Karttunen, <a href="/A346486/b346486.txt">Table of n, a(n) for n = 1..10000</a>
%H A346486 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A346486 a(1) = 1; and for n > 1, a(n) = A020639(n) * a(A302044(n)).
%F A346486 a(n) = A007947(A250246(n)) = A250246(n) / A346487(n).
%F A346486 For all n >= 1, A001221(a(n)) = A001222(a(n)) = A302041(n).
%o A346486 (PARI)
%o A346486 up_to = 65537;
%o A346486 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 A346486 A000265(n) = (n/2^valuation(n, 2));
%o A346486 A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);
%o A346486 v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
%o A346486 A078898(n) = v078898[n];
%o A346486 A302044(n) = { my(c = A000265(A078898(n))); if(1==c,1,my(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 A346486 A346486(n) = if(1==n,n,A020639(n)*A346486(A302044(n)));
%Y A346486 Cf. A000265, A001221, A001222, A007947, A020639, A078898, A250246, A302041, A302044, A346487.
%K A346486 nonn
%O A346486 1,2
%A A346486 _Antti Karttunen_, Aug 17 2021