A173618 Numbers k such that tau(phi(k)) = rad(k).

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

W. Sierpinski, Number Of Divisors And Their Sum

Wikipedia, Euler's totient function

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

Cf. A000005, A000010, A062069, A062821, A007947, A173326.

Sequence in context: A224094 A367511 A280934 * A091722 A053939 A167632

Adjacent sequences: A173615 A173616 A173617 * A173619 A173620 A173621

Keyword

nonn

Author

Michel Lagneau, Feb 22 2010

Extensions

a(30)-a(37) from Donovan Johnson, Jul 27 2011

Status

approved