

A121850


Numbers n such that (phi(n) + sigma(n))/(rad(n))^2 is an integer, that is (phi(n) + sigma(n)) is divisible by every prime factor of n squared.


1



1, 2, 588, 864, 2430, 7776, 27000, 55296, 69984, 82134, 215622, 432000, 497664, 629856, 675000, 862488, 1499136, 1749600, 2187000, 2667168, 3449952, 3538944, 4287500, 4312440, 4478976, 4563000, 5668704, 6912000, 10800000, 13045131
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OFFSET

1,2


REFERENCES

J.M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 71, entry 588.


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}]


CROSSREFS

Cf. a(n) are numbers n such that A000010(n) + A000203(n) is divisible by A007947(n)^2. This sequence is similar to A097982.
Sequence in context: A129697 A214911 A203770 * A291320 A100011 A172892
Adjacent sequences: A121847 A121848 A121849 * A121851 A121852 A121853


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



