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A268373 Numbers other than prime powers divisible by the sum of the cubes of their prime divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Koninck & Luca prove that this set is infinite. - Charles R Greathouse IV, Feb 03 2016
LINKS
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
Sequence in context: A349539 A098835 A134602 * A030029 A064242 A116339
KEYWORD
nonn
AUTHOR
Michel Marcus, Feb 03 2016
STATUS
approved

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Last modified April 20 00:00 EDT 2024. Contains 371798 sequences. (Running on oeis4.)