login
A173744
Numbers n such that tau(phi(n))= phi(rad(n))
1
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.
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 23 2010; corrected Feb 27 2010
EXTENSIONS
Corrected by Harvey P. Dale, Oct 24 2017
STATUS
approved