A173744 Numbers n such that tau(phi(n))= phi(rad(n))

1, 2, 3, 6, 20, 28, 45, 75, 90, 147, 150, 169, 176, 189, 208, 252, 294, 336, 338, 378, 480, 608, 792, 875, 1400, 1444, 1521, 1715, 1750, 1960, 2808, 2904, 3042, 3159, 3430, 3744, 4056, 4624, 6318, 6591, 6859, 8448, 11016, 13182, 13718, 14700, 16900

Offset

1,2

Comments

Here rad(n) is the product of the primes dividing n (A007947), tau(n) is the number of divisors of n (A000005), phi(n): Euler totient function (A000010)

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

Harvey P. Dale, Table of n, a(n) for n = 1..300

W. Sierpinski, Number Of Divisors And Their Sum

Wikipedia, Euler's totient function

Formula

Numbers n such that A000005(A000010)(n) = A000010(A007947)(n)

Example

for n=3,phi(3) = 2, tau(2)=2, rad(3)=3 and phi(3) = 2 for n=18900,phi(18900) =4320,tau(4320)= 48, rad(18900)=210, and phi(210) = 48

Maple

with(numtheory):for n from 1 to 20000 do: t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n))= phi(t2)then print (n): else fi: od :

Mathematica

Select[Range[17000], DivisorSigma[0, EulerPhi[#]]==EulerPhi[Times @@ FactorInteger[ #][[All, 1]]]&] (* Harvey P. Dale, Oct 24 2017 *)

Crossrefs

Sequence in context: A328218 A254441 A336461 * A227316 A176806 A323464

Adjacent sequences: A173741 A173742 A173743 * A173745 A173746 A173747

Keyword

nonn

Author

Michel Lagneau, Feb 23 2010; corrected Feb 27 2010

Extensions

Corrected by Harvey P. Dale, Oct 24 2017

Status

approved