A173326 - OEIS

%I #30 Apr 01 2019 03:01:21

%S 4,8,32,1344,2016,2025,2376,3375,3528,4032,4224,4704,4752,5292,5376,

%T 5625,6084,6804,7128,9408,9504,10125,10206,10935,12100,12348,12672,

%U 16875,16896,20412,21384,23814,26136,28512,29952,30375,31944,32832,42768,46464,48114

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

%H Donovan Johnson, <a href="/A173326/b173326.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Bogomolny, <a href="http://www.cut-the-knot.org/blue/Euler.shtml">Euler Function and Theorem</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>

%F {k: A163109(k) = A008472(k)}.

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

%e 8 is in the sequence because tau(8) = 4, phi(4) = 2 and sopf(8) = 2.

%p A008472 := proc(n) add(p,p= numtheory[factorset](n)) ; end proc:

%p A163109 := proc(n) numtheory[phi](numtheory[tau](n)) ; end proc:

%p for n from 1 to 40000 do if A008472(n) = A163109(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Sep 02 2011

%t Select[Range[2,50000],EulerPhi[DivisorSigma[0,#]]==Total[ Transpose[ FactorInteger[#]][[1]]]&] (* _Harvey P. Dale_, Nov 15 2013 *)

%Y Cf. A000005 (tau), A000010 (phi), A008472 (sopf).

%Y Cf. A173320, A062069, A001414, A001222.

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 16 2010

%E Corrected and edited by _Michel Lagneau_, Apr 25 2010