A366295 - OEIS

%I #8 Oct 07 2023 21:39:48

%S 1,2,3,4,2,5,3,6,7,1,8,9,10,5,5,11,12,13,3,14,15,16,17,18,19,15,20,9,

%T 2,3,21,22,14,23,5,24,4,5,25,26,27,10,3,28,13,29,30,31,32,33,29,34,17,

%U 35,16,18,15,1,36,37,38,39,28,40,15,4,10,41,42,3,43,44,12,14,45,9,14,30,4,46,47,48,49,50,23,5,5

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A349623(i) = A349623(j) for all i, j >= 1, where A349623 is the Dirichlet inverse of A064989(sigma(A003961(n))).

%C Restricted growth sequence transform of A349623.

%H Antti Karttunen, <a href="/A366295/b366295.txt">Table of n, a(n) for n = 1..65537</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 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

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

%o A326042(n) = A064989(sigma(A003961(n)));

%o v366295 = rgs_transform(DirInverseCorrect(vector(up_to,n,A326042(n))));

%o A366295(n) = v366295[n];

%Y Cf. A000203, A003961, A064989, A326042, A349623.

%Y Cf. also A286603, A366294.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 07 2023