A373152 - OEIS

%I #6 Jun 03 2024 10:30:18

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

%T 17,12,2,18,19,2,2,8,13,2,2,2,7,10,2,2,20,21,22,23,11,2,24,8,13,12,2,

%U 2,3,2,2,25,26,27,2,2,11,12,2,2,28,2,2,22,29,27,2,2,20,30,2,2,3,12,2,8,13,2,10,31,7,12,2,18,32,2,33,10,34,2,2,2,13,2

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.

%C Restricted growth sequence transform of the ordered pair [A085731(n), A373145(n)], i.e., the ordered pair [gcd(n, A003415(n)), gcd(A003415(n), A276085(n))].

%C For all i, j >= 1: A373150(i) = A373150(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A373152/b373152.txt">Table of n, a(n) for n = 1..100000</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 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o Aux373152(n) = [gcd(n, A003415(n)), gcd(A003415(n), A276085(n))];

%o v373152 = rgs_transform(vector(up_to, n, Aux373152(n)));

%o A373152(n) = v373152[n];

%Y Cf. A085731, A276085, A373145.

%Y Cf. also A373150, A373151.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 03 2024