A329035 - OEIS

%I #6 Nov 08 2019 18:16:03

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

%T 17,10,18,8,7,5,19,9,20,21,22,4,23,7,24,11,25,21,26,27,28,8,29,10,30,

%U 27,31,13,32,1,33,16,34,5,35,7,36,9,37,38,39,40,41,17,42,11,43,8,44,27,45,19,46,6,47,22,48,49,50,10,51,13,52,23,53,54,55,56,57,58,59,9

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A329034(i) = A329034(j) for all i, j, where A329034 is the Möbius transform of A122111.

%C Restricted growth sequence transform of A329034.

%H Antti Karttunen, <a href="/A329035/b329035.txt">Table of n, a(n) for n = 1..65537</a>

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

%o (PARI)

%o up_to = 8192;

%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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A329034(n) = sumdiv(n,d,moebius(n/d)*A122111(d));

%o v329035 = rgs_transform(vector(up_to, n, A329034(n)));

%o A329035(n) = v329035[n];

%Y Cf. A008683, A122111, A329034.

%K nonn

%O 1,3

%A _Antti Karttunen_, Nov 08 2019