A173328 - OEIS

%I #17 Jul 12 2019 01:30:43

%S 4,6,8,9,10,12,18,20,22,25,27,30,32,34,44,49,50,58,60,68,70,82,90,102,

%T 104,105,116,118,121,125,135,140,142,150,152,164,169,174,182,189,190,

%U 195,202,204,208,214,231,236,238,242,243,246,248,252,274,284,285,286

%N Numbers k such that phi(tau(k)) = tau(sopf(k)).

%C Sopf = A008472 is the sum of the distinct primes dividing n, tau= A000005 is the number of divisors, phi = A000010 is Euler's totient.

%H Harvey P. Dale, <a href="/A173328/b173328.txt">Table of n, a(n) for n = 1..1000</a>

%H P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113.

%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf"> Number Of Divisors And Their Sum</a>, Elementary theory of numbers, Warszawa, 1964.

%F {n : A163109(n)= tau(A008472(n))}.

%e 4 is in the sequence because tau(4) = 3, phi(3)=2, sopf(4)=2 and tau(2) = 2;

%e 6 is in the sequence because tau(6) = 4, phi(6)=2, sopf(6)=5 and tau(5) = 2.

%p isA173328 := proc(n)

%p         numtheory[phi](numtheory[tau](n)) = numtheory[tau](A008472(n)) ;

%p end proc:

%p for n from 1 to 300 do

%p         if isA173328(n) then

%p                 printf("%d,",n);

%p         end if;

%p end do: # _R. J. Mathar_, Nov 07 2011

%t Select[Range[2,300],EulerPhi[DivisorSigma[0,#]]==DivisorSigma[0, Total[ FactorInteger[#][[All,1]]]]&] (* _Harvey P. Dale_, May 30 2017 *)

%Y Cf. A008472 (sopfr).

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 16 2010