A323240 - OEIS

%I #12 Jan 11 2019 20:36:15

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,3,10,2,11,2,12,13,14,2,15,16,17,18,19,2,

%T 8,2,20,21,22,23,24,2,25,26,15,2,27,2,28,29,30,2,31,26,32,33,34,2,35,

%U 36,37,26,38,2,39,2,40,41,42,43,44,2,45,46,47,2,48,2,49,8,50,51,52,2,53,54,55,2,56,57,58,59,60,2,61,62,63,64,65,66,67,2,68,69,60,2

%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = [A001222(n), A323244(n)] for n > 1, and f(1) = 0.

%C Restricted growth sequence transform of function f, where f(1) = 0 and f(n) = [A001222(n), A323244(n)] for n > 1.

%C Equally, restricted growth sequence transform of function f, where f(1) = 0 and f(n) = A318310(A156552(n)) for n > 1.

%C For all i, j:

%C   a(i) = a(j) => A323245(i) = A323245(j), [Equally: A323244(i) = A323244(j)]

%C   a(i) = a(j) => A323246(i) = A323246(j). [Equally: A323248(i) = A323248(j)]

%H Antti Karttunen, <a href="/A323240/b323240.txt">Table of n, a(n) for n = 1..4096</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</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 A323240aux(n) = if(1==n,-1,[bigomega(n),A323244(n)]);

%o v323240 = rgs_transform(vector(up_to, n, A323240aux(n)));

%o A323240(n) = v323240[n];

%Y Cf. A001222, A156552, A318310, A323244, A323245, A323246, A323248.

%Y Cf. also A323168.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 10 2019