A173745 Numbers n such that tau(phi(n)) = sigma(rad(n)).

1, 8, 9, 25, 49, 216, 288, 324, 675, 1125, 1331, 1458, 1568, 2000, 2744, 3200, 3645, 6125, 6144, 8575, 9604, 9801, 14336, 30976, 31250, 42592, 46875, 70304, 72171, 81000, 108000, 109375, 123201, 129600, 131769, 135000, 145800, 182250, 184832

Offset: 1

Author

Michel Lagneau, Feb 23 2010

Keywords

• nonn

Comments

tau(phi(n)) = A000005(A000010(n)) = A062821(n).

sigma(rad(n)) = A000203(A007947(n)) = A048250(n).

Examples

			For n=9, tau(phi(9)) = tau(6)=4 equals sigma(rad(9)) = sigma(3) = 4 which adds n=9 to the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100
• W. Sierpinski, Number Of Divisors And Their Sum, Monogr. Matemat. 42 (1964) chapter IV

Programs

Magma

[1] cat [m:m in [2..200000]|#Divisors(EulerPhi(m)) eq &+Divisors(&*PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019

Maple

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 :

Mathematica

Select[Range[200000], DivisorSigma[0,EulerPhi[#]] == DivisorSigma[1, Times @@ FactorInteger[#][[All,1]]] & ] (* Jean-François Alcover, Sep 12 2011 *)

PARI

isok(n) = numdiv(eulerphi(n)) == sigma(factorback(factorint(n)[, 1])); \\ Michel Marcus, Jul 10 2019

Formula

{ n : A062821(n) = A048250(n) }.

Extensions

Unspecific references removed by R. J. Mathar, Mar 26 2010