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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. 3

%I

%S 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 39,40,42,44,45,46,48,49,50,51,52,54,56,57,58,60,62,63,64,65,66,68,69,

%U 70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,91,92,93,94,96,98,99

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

%o (MATLAB)

%o n=100; % gives all terms of the sequence not exceeding n

%o A=[];

%o for i=1:n

%o dn=divisors(i);

%o if size(dn,2)>2 && mod(totient(i)/totient(dn(2)),totient(i)/totient(dn(end-1)))==0

%o A=[A i];

%o end

%o end

%o function [res] = totient(n)

%o res=0;

%o for i=1:n

%o if gcd(i,n)==1

%o res=res+1;

%o end

%o end

%o end

%o (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 Cf. A000010, A002808, A335902.

%K nonn

%O 1,1

%A _Maxim Karimov_, Dec 27 2020

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)