

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
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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
JeanMarie 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. 557563.


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: A045197 A098835 A134602 * A030029 A064242 A116339
Adjacent sequences: A268370 A268371 A268372 * A268374 A268375 A268376


KEYWORD

nonn


AUTHOR

Michel Marcus, Feb 03 2016


STATUS

approved



