A340058 Composite numbers c such that phi(c)/phi(mind(c)) mod phi(c)/phi(maxd(c)) = 0, where phi is the Euler function, mind(c) is the smallest nontrivial divisor of c, maxd(c) is the largest nontrivial divisor of c.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 98, 99

Offset: 1

Author

Maxim Karimov, Dec 27 2020

Keywords

• nonn

Comments

This equivalence criterion splits a set of composite numbers into two classes and can be used to count certain combinatorial objects.

Crossrefs

Cf. A000010, A002808, A335902.

Programs

MATLAB

n=100; % gives all terms of the sequence not exceeding n
A=[];
for i=1:n
   dn=divisors(i);
   if size(dn,2)>2 && mod(totient(i)/totient(dn(2)),totient(i)/totient(dn(end-1)))==0
      A=[A i];
   end
end
function [res] = totient(n)
res=0;
    for i=1:n
        if gcd(i,n)==1
            res=res+1;
        end
    end
end

PARI

isok(c) = if ((c>1) && !isprime(c), my(t=eulerphi(c), d=divisors(c)); ((t/eulerphi(d[2])) % (t/eulerphi(d[#d-1]))) == 0); \\ Michel Marcus, Dec 28 2020