A365463 a(n) = gcd(n, A356867(n)), where A356867 is Sycamore's Doudna variant D(3).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 15 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..19683

Crossrefs

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

Cf. also A364500.

Programs

PARI

up_to = 19683;
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); };
v356867 = A356867list(up_to);
A356867(n) = v356867[n];
A365463(n) = gcd(n, A356867(n));

Formula

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

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

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