cp's OEIS Frontend

A335902 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 A335902 #47 Jan 01 2021 12:53:19
%S A335902 35,55,77,95,115,119,143,155,161,187,203,209,215,221,235,245,247,253,
%T A335902 287,295,299,319,323,329,335,355,371,377,391,395,403,407,413,415,437,
%U A335902 473,493,497,515,517,527,533,535,551,559,581,583,589,605,611,623,629,635,649
%N A335902 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 A335902 This equivalence criterion splits a set of composite numbers into two classes and can be used to count certain combinatorial objects.
%o A335902 (MATLAB)
%o A335902 n=500; % gives all terms of the sequence not exceeding n
%o A335902 A=[];
%o A335902 for i=1:n
%o A335902     dn=divisors(i);
%o A335902     if size(dn,2)>2 && mod (totient(i)/totient(dn(2)),totient(i)/totient(dn(end-1)))~=0
%o A335902         A=[A i];
%o A335902     end
%o A335902 end
%o A335902 function [res] = totient(n)
%o A335902 res=0;
%o A335902     for i=1:n
%o A335902         if gcd(i,n)==1
%o A335902             res=res+1;
%o A335902         end
%o A335902     end
%o A335902 end
%o A335902 (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 A335902 Cf. A000010, A002808, A340058.
%K A335902 nonn
%O A335902 1,1
%A A335902 _Maxim Karimov_, Dec 28 2020