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A173618
Numbers k such that tau(phi(k)) = rad(k).
1
1, 4, 36, 54, 96, 200, 448, 1280, 2700, 4500, 5103, 9720, 11264, 14112, 14580, 17280, 26624, 32928, 48000, 54432, 71442, 75000, 81648, 152064, 184320, 187500, 258048, 307200, 350000, 637875, 1250235, 1344560, 1557504, 2044416, 2187500, 2367488, 3234816
OFFSET
1,2
COMMENTS
rad(k) is the product of the primes dividing k (A007947), tau(k) is the number of divisors of k (A000005), phi(k) is the 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
k such that A062821(k) = A007947(k).
EXAMPLE
phi(4) = 2, tau(2) = 2 and rad(4) = 2 phi(36) = 12, tau(12) = 6 and rad(36) = 6
MAPLE
with(numtheory):for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n))= t2 then print (n): else fi: od :
MATHEMATICA
rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[10^5], DivisorSigma[0, EulerPhi[#]] == rad[#] &] (* Amiram Eldar, Jul 09 2019*)
PROG
(PARI) isok(k) = numdiv(eulerphi(k)) == factorback(factorint(k)[, 1]); \\ Michel Marcus, Jul 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 22 2010
EXTENSIONS
a(30)-a(37) from Donovan Johnson, Jul 27 2011
STATUS
approved