OFFSET
1,2
COMMENTS
This sequence is infinite because every integer m = 32 * 3^(2r+1), r>=1 is a term: 864, 7776, 69984, ... (see De Koninck & Mercier reference). - Bernard Schott, Dec 02 2020
REFERENCES
J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 71, entry 588.
J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Ellipses, 2004, Problème 749, pp. 95 and 319.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..145
EXAMPLE
For example, phi(588) = 168, sigma(588) = 1596, 588 = 2^2*3*7^2. The product of all prime divisors is 42, its square is 1764. Hence phi(588) + sigma(588), which is equal to 1764 is divisible by the square of each prime divisor of 588.
MATHEMATICA
Do[If[IntegerQ[(DivisorSigma[1, n] + EulerPhi[n])/(Times @@ Transpose[FactorInteger[n]][[1]])^2], Print[n]], {n, 1, 1000000}]
PROG
(PARI) isok(k) = (((eulerphi(k) + sigma(k)) % factorback(factorint(k)[, 1])^2) == 0); \\ Michel Marcus, Dec 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Aug 30 2006
EXTENSIONS
a(17)-a(30) from Donovan Johnson, Feb 05 2010
a(1) = 1 inserted by Amiram Eldar, Aug 24 2019
STATUS
approved