A373988 - OEIS

%I #6 Jun 25 2024 23:43:48

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

%T 15,16,17,2,2,18,19,4,2,20,2,21,8,22,2,8,2,23,24,25,2,6,26,27,28,29,2,

%U 2,2,30,31,4,32,33,2,34,35,36,2,2,2,37,38,39,3,40,2,14,2,41,2,38,42,43,44,15,2,38,45,46,47,48,49,2,2,50,51,17,2,52,2,19

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A373986(i) = A373986(j), for all i, j >= 1.

%C Restricted growth sequence transform of A373986.

%C For all i, j >= 1: A305800(i) = A305800(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A373988/b373988.txt">Table of n, a(n) for n = 1..100000</a>

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

%o (PARI)

%o up_to = 100000;

%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 A373986(n) = { my(f=factor(n),m=1,s=0); for(i=1, #f~, my(x=prod(i=1,primepi(f[i, 1]),prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); s/gcd(m,s); };

%o v373988 = rgs_transform(vector(up_to, n, A373986(n)));

%o A373988(n) = v373988[n];

%Y Cf. A108951, A373158, A373986.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 25 2024