|
%I #24 Sep 08 2022 08:45:50
%S 1,8,9,25,49,216,288,324,675,1125,1331,1458,1568,2000,2744,3200,3645,
%T 6125,6144,8575,9604,9801,14336,30976,31250,42592,46875,70304,72171,
%U 81000,108000,109375,123201,129600,131769,135000,145800,182250,184832
%N Numbers n such that tau(phi(n)) = sigma(rad(n)).
%C tau(phi(n)) = A000005(A000010(n)) = A062821(n).
%C sigma(rad(n)) = A000203(A007947(n)) = A048250(n).
%H Amiram Eldar, <a href="/A173745/b173745.txt">Table of n, a(n) for n = 1..100</a>
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>, Monogr. Matemat. 42 (1964) chapter IV
%F { n : A062821(n) = A048250(n) }.
%e For n=9, tau(phi(9)) = tau(6)=4 equals sigma(rad(9)) = sigma(3) = 4 which adds n=9 to the sequence.
%p with(numtheory):for n from 1 to 1500000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n)) = sigma(t2) then print (n): else fi: od :
%t Select[Range[200000], DivisorSigma[0,EulerPhi[#]] == DivisorSigma[1, Times @@ FactorInteger[#][[All,1]]] & ] (* _Jean-François Alcover_, Sep 12 2011 *)
%o (Magma) [1] cat [m:m in [2..200000]|#Divisors(EulerPhi(m)) eq &+Divisors(&*PrimeDivisors(m))]; // _Marius A. Burtea_, Jul 10 2019
%o (PARI) isok(n) = numdiv(eulerphi(n)) == sigma(factorback(factorint(n)[, 1])); \\ _Michel Marcus_, Jul 10 2019
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 23 2010
%E Unspecific references removed by _R. J. Mathar_, Mar 26 2010
|
