A173617 Numbers n such that phi(tau(n))= rad(n)

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

Table of n, a(n) for n=1..17.

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.

Wikipedia, Euler's totient function

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

Cf. A173320, A062069, A001414, A001222.

Sequence in context: A129195 A180098 A124143 * A034041 A378083 A050442

Adjacent sequences: A173614 A173615 A173616 * A173618 A173619 A173620

Keyword

nonn

Author

Michel Lagneau, Feb 22 2010

Extensions

a(14)-a(17) from Donovan Johnson, Jul 27 2011

Status

approved