A355832 - OEIS

%I #9 Jul 20 2022 15:59:10

%S 1,2,2,2,2,1,2,2,3,1,2,1,2,1,1,4,2,5,2,1,6,1,2,1,7,6,3,1,2,2,2,8,1,1,

%T 2,9,2,1,1,10,2,11,2,2,3,6,2,12,3,13,6,11,2,14,1,10,1,1,2,2,2,1,15,16,

%U 2,2,2,1,1,10,2,17,2,1,18,19,2,11,2,20,3,1,2,10,1,6,1,21,2,14,1,22,1,23,2,24,2,9,3,25,2,1,2,26,26

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A354347(i) = A354347(j) for all i, j >= 1.

%C Restricted growth sequence transform of A354347, which is the Dirichlet inverse of A345000(n) = gcd(A003415(n), A003415(A276086(n))).

%H Antti Karttunen, <a href="/A355832/b355832.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%o (PARI)

%o up_to = 65537;

%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 DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A345000(n) = gcd(A003415(n),A003415(A276086(n)));

%o v354347 = DirInverseCorrect(vector(up_to,n,A345000(n)));

%o v355832 = rgs_transform(v354347);

%o A355832(n) = v355832[n];

%Y Cf. A003415, A276086, A345000, A354347, A355831.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 19 2022