cp's OEIS Frontend

A305434 Restricted growth sequence transform of A285713, formed from the prime signature of A245612(n).

%I A305434 #5 Jun 01 2018 21:42:26
%S A305434 1,2,2,2,3,2,4,5,2,6,3,5,2,6,2,3,3,2,6,6,2,3,3,2,6,7,2,3,8,6,2,2,3,3,
%T A305434 9,2,2,10,3,11,6,2,12,7,3,3,9,3,3,9,2,13,3,2,6,14,3,9,2,3,6,3,6,5,3,3,
%U A305434 12,11,3,11,3,2,7,15,3,3,7,16,2,3,2,3,3,3,2,9,3,10,3,3,6,12,3,6,3,3,17,6,3,9,6,6,2,2,3,6
%N A305434 Restricted growth sequence transform of A285713, formed from the prime signature of A245612(n).
%H A305434 Antti Karttunen, <a href="/A305434/b305434.txt">Table of n, a(n) for n = 0..65537</a>
%o A305434 (PARI)
%o A305434 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A305434 A048673(n) = (A003961(n)+1)/2;
%o A305434 A254049(n) = A048673((2*n)-1);
%o A305434 A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
%o A305434 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305434 A285713(n) = A046523(A245612(n));
%o A305434 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 A305434 v305434 = rgs_transform(vector(65538,n,A285713(n-1)));
%o A305434 A305434(n) = v305434[1+n];
%Y A305434 Cf. A046523, A245612, A285713.
%Y A305434 Cf. also A305433.
%K A305434 nonn
%O A305434 0,2
%A A305434 _Antti Karttunen_, Jun 01 2018