login
A173617
Numbers n such that phi(tau(n))= rad(n)
0
1, 4, 8, 32, 36, 192, 288, 768, 972, 1458, 5120, 13122, 326592, 19531250, 22588608, 46137344, 171532242
OFFSET
1,2
COMMENTS
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)
a(18) > 10^10. - Donovan Johnson, Jul 27 2011
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
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 such that A163109(n)= A007947(n)
EXAMPLE
tau(8) = 4, phi(4)=2 and rad(8)=2 tau(13122) = 18, phi(18)=6 and rad(13122)=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 phi(tau(n)) = t2 then print (n): else fi : od :
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 22 2010
EXTENSIONS
a(14)-a(17) from Donovan Johnson, Jul 27 2011
STATUS
approved