A329045 - OEIS

%I #7 Nov 08 2019 18:16:33

%S 1,2,2,3,2,3,2,4,4,3,2,5,2,3,6,7,2,7,2,5,6,3,2,8,9,3,4,5,2,10,2,4,6,3,

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

%U 17,18,2,5,6,19,2,20,2,3,21,5,22,18,2,7,13,3,2,7,23,3,6,15,2,24,25,5,6,3,26,27,2,28,24,13,2,18,2,15,29

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A329044(i)) = A046523(A329044(j)) for all i, j.

%C Restricted growth sequence transform of function f(n) = A046523(A329044(n)).

%C For all i, j:

%C   A305800(i) = A305800(j) => a(i) = a(j),

%C   a(i) = a(j) => A324888(i) = A324888(j),

%C   a(i) = a(j) => A329046(i) = A329046(j).

%H Antti Karttunen, <a href="/A329045/b329045.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>

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

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</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 A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

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

%o A324886(n) = A276086(A108951(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 A329044(n) = A064989(A324886(n));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o v329045 = rgs_transform(vector(up_to, n, A046523(A329044(n))));

%o A329045(n) = v329045[n];

%Y Cf. A034386, A064989, A108951, A276086, A305800, A324886, A324888, A329044, A329046.

%Y Cf. also A278226, A286626.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 08 2019