A173328 Numbers k such that phi(tau(k)) = tau(sopf(k)).

4, 6, 8, 9, 10, 12, 18, 20, 22, 25, 27, 30, 32, 34, 44, 49, 50, 58, 60, 68, 70, 82, 90, 102, 104, 105, 116, 118, 121, 125, 135, 140, 142, 150, 152, 164, 169, 174, 182, 189, 190, 195, 202, 204, 208, 214, 231, 236, 238, 242, 243, 246, 248, 252, 274, 284, 285, 286

Offset

1,1

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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, Elementary theory of numbers, Warszawa, 1964.

Formula

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

Example

4 is in the sequence because tau(4) = 3, phi(3)=2, sopf(4)=2 and tau(2) = 2;
6 is in the sequence because tau(6) = 4, phi(6)=2, sopf(6)=5 and tau(5) = 2.

Maple

isA173328 := proc(n)
        numtheory[phi](numtheory[tau](n)) = numtheory[tau](A008472(n)) ;
end proc:
for n from 1 to 300 do
        if isA173328(n) then
                printf("%d, ", n);
        end if;
end do: # R. J. Mathar, Nov 07 2011

Mathematica

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

Crossrefs

Cf. A008472 (sopfr).

Sequence in context: A047820 A248807 A034878 * A116661 A109104 A073303

Adjacent sequences: A173325 A173326 A173327 * A173329 A173330 A173331

Keyword

nonn

Author

Michel Lagneau, Feb 16 2010

Status

approved