A323245 - OEIS

%I #8 Jan 11 2019 20:36:39

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,3,5,2,10,2,11,12,11,2,13,14,15,4,13,2,8,

%T 2,16,17,18,19,17,2,20,21,13,2,22,2,23,24,25,2,15,21,26,24,27,2,28,29,

%U 30,21,31,2,32,2,33,9,13,8,32,2,34,35,36,2,37,2,38,8,39,40,41,2,42,21,43,2,44,45,46,47,16,2,10,48,49,50,51,52,30,2,53,14,16,2

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A323244(n) for n > 1, and f(1) = -1.

%C Restricted growth sequence transform of function f, defined as f(1) = -1, and for n > 1, f(n) = A033879(A156552(n)).

%H Antti Karttunen, <a href="/A323245/b323245.txt">Table of n, a(n) for n = 1..4096</a>

%o (PARI)

%o up_to = 1024;

%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 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));

%o A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));

%o A323245aux(n) = if(1==n,-1,A323244(n));

%o v323245 = rgs_transform(vector(up_to, n, A323245aux(n)));

%o A323245(n) = v323245[n];

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 10 2019