%I A055465
%S A055465 1,4,15,21,25,30,33,35,39,45,48,49,51,55,56,57,65,69,70,77,78,81,85,87,
%T A055465 91,93,95,99,102,105,110,111,115,119,121,123,125,126,129,133,135,140,
%U A055465 141,143,145,147,153,155,159,161,165,168,169,174,177,180,182,183,184
%N A055465 Composite numbers for which sum of EulerPhi and Divisor-Sum is an integer 
               multiple of the number of divisors.
%C A055465 Makowski proved that Phi[n]+Sigma[n] = nd[n] iff n is a prime (see in 
               Sivaramakrishnan,Chapter I, page 8, Theorem 3) In more general case 
               k differs from n.
%D A055465 Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions 
               Marcel Dekker,Inc., New York-Basel.
%F A055465 Composite integer solutions of Phi[x]+Sigma[x] = kd[x] or A000203(n)+A000010(n) 
               = k*A000005(n), where k is integer.
%e A055465 It is true for all primes and some composites. n = 78, 8 divisors, Sigma 
               = 168, Phi = 24, 168+24 = 192 = 8*24
%Y A055465 Sequence in context: A166732 A022133 A100783 this_sequence A167293 A054308 
               A051531
%Y A055465 Adjacent sequences: A055462 A055463 A055464 this_sequence A055466 A055467 
               A055468
%K A055465 nonn
%O A055465 1,2
%A A055465 Labos E. (labos(AT)ana.sote.hu), Jun 27 2000