A173326 Numbers k such that phi(tau(k)) = sopf(k).

4, 8, 32, 1344, 2016, 2025, 2376, 3375, 3528, 4032, 4224, 4704, 4752, 5292, 5376, 5625, 6084, 6804, 7128, 9408, 9504, 10125, 10206, 10935, 12100, 12348, 12672, 16875, 16896, 20412, 21384, 23814, 26136, 28512, 29952, 30375, 31944, 32832, 42768, 46464, 48114

Offset: 1

Author

Michel Lagneau, Feb 16 2010

Keywords

• nonn

Examples

			4 is in the sequence because tau(4) = 3, phi(3) = 2 and sopf(4) = 2.
8 is in the sequence because tau(8) = 4, phi(4) = 2 and sopf(8) = 2.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• A. Bogomolny, Euler Function and Theorem
• P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., 19 (1919), 75-113.
• W. Sierpinski, Number Of Divisors And Their Sum

Crossrefs

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

Cf. A173320, A062069, A001414, A001222.

Programs

Maple

A008472 := proc(n) add(p,p= numtheory[factorset](n)) ; end proc:
A163109 := proc(n) numtheory[phi](numtheory[tau](n)) ; end proc:
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

Mathematica

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

Formula

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

Extensions

Corrected and edited by Michel Lagneau, Apr 25 2010