A355830 - OEIS

%I #8 Jul 20 2022 18:43:38

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

%T 15,4,4,16,17,2,4,4,18,2,14,2,19,20,10,2,21,6,22,10,19,2,23,4,18,4,4,

%U 2,24,2,4,20,25,16,14,2,7,4,14,2,26,2,4,27,28,16,14,2,29,30,4,2,24,4,10,4,31,2,32,4,33,4,34,16,35,2,36,20,37,2,38,2,18,14

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A345000(i) = A345000(j) for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A046523(n), A345000(n)].

%C For all i, j: A351235(i) = A351235(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A355830/b355830.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 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

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

%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 Aux355830(n) = [A046523(n), A345000(n)];

%o v355830 = rgs_transform(vector(up_to,n,Aux355830(n)));

%o A355830(n) = v355830[n];

%Y Cf. A003415, A046523, A276086, A345000.

%Y Cf. also A351235, A355000, A355831, A355832, A355836.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 20 2022