Search: id:A055464
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%I A055464
%S A055464 1,2,3,4,5,7,11,13,15,17,19,21,23,25,29,30,31,33,35,37,39,41,43,45,47,
%T A055464 48,49,51,53,55,56,57,59,61,65,67,69,70,71,73,77,78,79,81,83,85,87,89,
%U A055464 91,93,95,97,99,101,102,103,105,107,109,110,111,113,115,119,121,123
%N A055464 Numbers n such that sum of EulerPhi and DivisorSum is an integer multiple 
               of the number of divisors.
%C A055464 Makowski proved that Phi[n]+Sigma[n] = nd[n] iff n is a prime (see in 
               Sivaramakrishnan,Chapter I, page 8, Theorem 3)
%D A055464 Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions 
               Marcel Dekker,Inc., New York-Basel.
%F A055464 Solutions to Phi[x]+Sigma[x] = kd[x] or A000203(n)+A000010(n) = k*A000005(n), 
               where k is integer.
%e A055464 It is true for all primes and some composites. n = 99, 6 divisors, Sigma 
               = 156, Phi = 60, 156+60 = 216 = 6*36, k = 36
%Y A055464 Sequence in context: A130080 A001729 A001087 this_sequence A139316 A062972 
               A036844
%Y A055464 Adjacent sequences: A055461 A055462 A055463 this_sequence A055465 A055466 
               A055467
%K A055464 nonn
%O A055464 1,2
%A A055464 Labos E. (labos(AT)ana.sote.hu), Jun 27 2000

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