A173743 Numbers k such that phi(tau(k)) = tau(rad(k)).

1, 4, 8, 9, 24, 25, 27, 32, 40, 48, 49, 54, 56, 72, 80, 88, 96, 104, 108, 112, 120, 121, 125, 135, 136, 152, 160, 162, 168, 169, 176, 184, 189, 200, 208, 224, 232, 240, 243, 248, 250, 264, 270, 272, 280, 289, 296, 297, 304, 312, 328, 336, 343, 344, 351, 352, 360

Offset

1,2

Comments

rad(n) = A007947(n). tau(n) = A000005(n). phi(n) = A000010(n). tau(rad(n)) = A034444(n).

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

W. Sierpinski, Number Of Divisors And Their Sum

Wikipedia, Euler's totient function

Formula

{ n : A163109(n) = A034444(n) }.

Example

For n=4, phi(tau(4)) = phi(3)=2 equals tau(rad(4)) = tau(2) = 2, so n=4 is in the sequence.
For n=108, phi(tau(108) ) = phi(12) = 4 equals tau(rad(108)) = tau(6) = 4, so n =108 is in the sequence.

Maple

with(numtheory): for n from 1 to 500 do :t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)):if phi(tau(n)) = tau(t2) then print (n): else fi:od:

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[360], EulerPhi[ DivisorSigma[0, #] ] == DivisorSigma[0, rad[#]] &] (* Amiram Eldar, Jul 09 2019 *)

Prog

(Magma) [ k:k in [1..360]| EulerPhi(#Divisors(k)) eq #Divisors(&*PrimeDivisors(k)) ]; // Marius A. Burtea, Jul 09 2019

Crossrefs

Cf. A000010, A000005, A007947, A034444, A163109.

Sequence in context: A213015 A064393 A372034 * A035326 A180865 A063907

Adjacent sequences: A173740 A173741 A173742 * A173744 A173745 A173746

Keyword

nonn

Author

Michel Lagneau, Feb 23 2010

Status

approved