A292582 - OEIS

%I #29 Feb 26 2018 18:57:55

%S 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,

%T 1,6,1,1,1,3,1,1,1,2,2,1,1,4,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,7,1,1,1,2,

%U 1,1,1,8,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1,3,1,2,1,2,1,1,1,5,1,2,2,6,1,1,1,3,1,1,1,8,1,1,1,4,1,1,1,2,2,1,1,3

%N Restricted growth sequence transform of A292589(n); filter based on the prime signature of {n divided by largest squarefree divisor of n}.

%C Also a restricted growth sequence transform of A278222(A292380(n)): a filter constructed from the runlengths of multiples of 4 encountered in trajectories of A005940-tree.

%H Antti Karttunen, <a href="/A292582/b292582.txt">Table of n, a(n) for n = 1..65536</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%o (PARI)

%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 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o write_to_bfile(1,rgs_transform(vector(16384,n,A046523(A003557(n)))),"b292582.txt");

%Y Cf. A003557, A005940, A046523, A083399, A278222, A292380, A292583, A292585, A292586, A292587, A292589.

%K nonn

%O 1,4

%A _Antti Karttunen_, Sep 25 2017