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

1,1

Comments

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

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A066031, A190882.

Sequence in context: A349539 A098835 A134602 * A030029 A064242 A116339

Adjacent sequences: A268370 A268371 A268372 * A268374 A268375 A268376

Keyword

nonn

Author

Michel Marcus, Feb 03 2016

Status

approved