A268373 Numbers other than prime powers divisible by the sum of the cubes of their prime divisors.

378, 480, 756, 960, 1134, 1440, 1512, 1920, 2268, 2400, 2548, 2646, 2880, 3024, 3402, 3840, 4320, 4536, 4800, 5096, 5292, 5760, 6048, 6804, 7200, 7680, 7938, 8640, 9072, 9600, 10192, 10206, 10584, 11520, 12000, 12096, 12960, 13608, 14400, 15360, 15876, 17280, 17836, 18144, 18522, 18711

Offset: 1

Author

Michel Marcus, Feb 03 2016

Keywords

• nonn

Comments

Koninck & Luca prove that this set is infinite. - Charles R Greathouse IV, Feb 03 2016

Examples

			The prime factors of 480 are 2, 3 and 5. The sum of their cubes is 2^3+3^3+5^3=160, and 480 is divisible by 160.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jean-Marie de Koninck, Florian Luca, Integers divisible by sums of powers of their prime factors, Journal of Number Theory, Volume 128, Issue 3 (March 2008), pp. 557-563.

Crossrefs

Cf. A066031, A190882.

Programs

Mathematica

Select[Range[10^4], Length[(p = FactorInteger[#][[;;,1]])] > 1 && Divisible[#, Total[p^3]] &] (* Amiram Eldar, Sep 05 2019 *)

PARI

isok(n) = my(f = factor(n)[,1]) ; (#f>2) && ((n % sum(k=1, #f, f[k]^3)) == 0);