cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A268373 #17 Sep 08 2019 10:05:29
%S A268373 378,480,756,960,1134,1440,1512,1920,2268,2400,2548,2646,2880,3024,
%T A268373 3402,3840,4320,4536,4800,5096,5292,5760,6048,6804,7200,7680,7938,
%U A268373 8640,9072,9600,10192,10206,10584,11520,12000,12096,12960,13608,14400,15360,15876,17280,17836,18144,18522,18711
%N A268373 Numbers other than prime powers divisible by the sum of the cubes of their prime divisors.
%C A268373 Koninck & Luca prove that this set is infinite. - _Charles R Greathouse IV_, Feb 03 2016
%H A268373 Amiram Eldar, <a href="/A268373/b268373.txt">Table of n, a(n) for n = 1..10000</a>
%H A268373 Jean-Marie de Koninck, Florian Luca, <a href="https://doi.org/10.1016/j.jnt.2007.01.010">Integers divisible by sums of powers of their prime factors</a>, Journal of Number Theory, Volume 128, Issue 3 (March 2008), pp. 557-563.
%e A268373 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.
%t A268373 Select[Range[10^4], Length[(p = FactorInteger[#][[;;,1]])] > 1 && Divisible[#, Total[p^3]] &] (* _Amiram Eldar_, Sep 05 2019 *)
%o A268373 (PARI) isok(n) = my(f = factor(n)[,1]) ; (#f>2) && ((n % sum(k=1, #f, f[k]^3)) == 0);
%Y A268373 Cf. A066031, A190882.
%K A268373 nonn
%O A268373 1,1
%A A268373 _Michel Marcus_, Feb 03 2016