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

1,1

Comments

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

Links

Table of n, a(n) for n=1..69.

Prog

(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

Crossrefs

Cf. A000010, A002808, A335902.

Sequence in context: A140209 A077091 A340268 * A174891 A051035 A046349

Adjacent sequences: A340055 A340056 A340057 * A340059 A340060 A340061

Keyword

nonn

Author

Maxim Karimov, Dec 27 2020

Status

approved