cp's OEIS Frontend

A328651 Composite k for which lcm(k, phi(k)) + lcm(k, tau(k)) = lcm(k, sigma(k)).

%I A328651 #22 Sep 08 2022 08:46:24
%S A328651 135,546,672,9585,24570,51510,63855,190008,251370,323730,372438,
%T A328651 486180,510570,723550,819000,1058910,1282365,1284192,1356030,3506390,
%U A328651 5416200,5604480,6298625,15593760,17813250,18009000,20740590,26759370,27027000,27081000,29795040
%N A328651 Composite k for which lcm(k, phi(k)) + lcm(k, tau(k)) = lcm(k, sigma(k)).
%C A328651 Composite numbers k verifying equation A009230(k) + A009262(k) = A009242(k).
%C A328651 For any prime number p >= 3 the equality lcm(k, phi(k)) + lcm(k, tau(k)) = lcm(k, sigma(k)) is satisfied.
%C A328651 The sequence terms are the composite numbers for which the equality is true.
%e A328651 For k = 135 = 3^3 * 5, tau(k) = 4 * 2 = 2^3, phi(k) = 2 * 3^2 * 4 = 2^3 * 3^2 , sigma(k) = 2^4 * 3 * 5, lcm(k, tau(k)) + lcm(k, phi(k)) =  2^3 * 3^3 * 5 + 2^3 * 3^3 * 5 = 2^4 * 3^3 * 5 and lcm(k, sigma(k)) = lcm(3^3 * 5, 2^4 * 3 * 5) = 2^4 * 3^3 * 5.
%t A328651 aQ[n_] := CompositeQ[n] && LCM[n, EulerPhi[n]] + LCM[n, DivisorSigma[0, n]] == LCM[n, DivisorSigma[1, n]]; Select[Range[3*10^6], aQ] (* _Amiram Eldar_, Oct 23 2019 *)
%o A328651 (Magma) [k: k in [1..6000000]| not IsPrime(k) and Lcm(k,NumberOfDivisors(k))+Lcm(k,EulerPhi(k)) eq Lcm(k,SumOfDivisors(k))];
%o A328651 (PARI) isok(k) = !isprime(k) && (lcm(k, numdiv(k)) + lcm(k, eulerphi(k)) == lcm(k, sigma(k))); \\ _Michel Marcus_, Oct 24 2019
%Y A328651 Cf. A000005, A000010, A000203, A009242, A009230, A009262, A326416.
%K A328651 nonn
%O A328651 1,1
%A A328651 _Marius A. Burtea_, Oct 23 2019