cp's OEIS Frontend

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.

%I A340058 #45 Jan 01 2021 12:54:14
%S A340058 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,36,38,
%T A340058 39,40,42,44,45,46,48,49,50,51,52,54,56,57,58,60,62,63,64,65,66,68,69,
%U A340058 70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,91,92,93,94,96,98,99
%N 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.
%C A340058 This equivalence criterion splits a set of composite numbers into two classes and can be used to count certain combinatorial objects.
%o A340058 (MATLAB)
%o A340058 n=100; % gives all terms of the sequence not exceeding n
%o A340058 A=[];
%o A340058 for i=1:n
%o A340058    dn=divisors(i);
%o A340058    if size(dn,2)>2 && mod(totient(i)/totient(dn(2)),totient(i)/totient(dn(end-1)))==0
%o A340058       A=[A i];
%o A340058    end
%o A340058 end
%o A340058 function [res] = totient(n)
%o A340058 res=0;
%o A340058     for i=1:n
%o A340058         if gcd(i,n)==1
%o A340058             res=res+1;
%o A340058         end
%o A340058     end
%o A340058 end
%o A340058 (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
%Y A340058 Cf. A000010, A002808, A335902.
%K A340058 nonn
%O A340058 1,1
%A A340058 _Maxim Karimov_, Dec 27 2020