A297162 - OEIS

%I #7 Dec 28 2017 19:34:56

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

%T 16,17,18,8,4,9,19,10,20,21,22,4,23,7,12,11,24,25,5,9,26,8,27,9,18,28,

%U 29,13,30,31,32,15,18,33,34,5,35,10,36,31,37,17,38,16,14,11,5,7,39,40,25,19,41,42,43,22,44,45,46,14,20,13,47,23

%N Restricted growth sequence transform of A297172, which is Möbius transform of A253564.

%H Antti Karttunen, <a href="/A297162/b297162.txt">Table of n, a(n) for n = 1..8192</a>

%o (PARI)

%o up_to = 8192;

%o rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,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 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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

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

%o A253564(n) = A156552(A122111(n));

%o A297172(n) = sumdiv(n,d,moebius(n/d)*A253564(d));

%o write_to_bfile(1,rgs_transform(vector(up_to,n,A297172(n))),"b297162.txt");

%Y Cf. A253564, A297172.

%Y Cf. also A297113, A297157, A297161.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 27 2017