A365463 - OEIS

%I #12 Sep 17 2023 10:06:44

%S 1,2,3,1,1,6,1,8,9,1,1,3,1,2,3,2,1,18,1,4,3,1,1,24,25,2,27,1,1,3,1,4,

%T 3,2,7,9,1,2,3,5,1,6,1,4,9,1,1,6,1,50,3,4,1,54,11,2,3,1,1,12,1,2,9,1,

%U 5,3,1,4,3,10,1,72,1,2,75,1,1,6,1,16,81,1,1,3,5,2,3,2,1,9,91,2,3,1,5,12,1,2,9,5,1,6,1,8,21

%N a(n) = gcd(n, A356867(n)), where A356867 is Sycamore's Doudna variant D(3).

%H Antti Karttunen, <a href="/A365463/b365463.txt">Table of n, a(n) for n = 1..19683</a>

%F a(n) = gcd(n, A365462(n)) = gcd(A356867(n), A365462(n)).

%F a(n) = n / A365464(n) = A356867(n) / A365465(n).

%F For all n >= 1, A007949(a(n)) = A007949(n), A011655(a(n)) = A011655(n).

%o (PARI)

%o up_to = 19683;

%o A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==vecsum(digits(i,3)), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };

%o v356867 = A356867list(up_to);

%o A356867(n) = v356867[n];

%o A365463(n) = gcd(n, A356867(n));

%Y Cf. A007949, A356867, A364957 (Dirichlet inverse), A365462, A365464, A365465.

%Y Cf. also A364500.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 15 2023