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%I #26 Feb 23 2020 06:42:06
%S 1,10,49,56,69,76,122,133,568,578,1001,1018,1243,1324,1431,1611,1685,
%T 1819,1994,2296,2323,3344,3403,3627,3641,3763,3981,4336,5482,8186,
%U 9077,9641,10113,10688,13471,14188,14509,14727,15940,16697,17141,17619,19241,19637
%N Nonprime numbers k such that sum of aliquot divisors of k is a cube.
%C The sum of the aliquot divisors of a prime is exactly 1. - _Martin Renner_, Oct 13 2011
%H Amiram Eldar, <a href="/A048698/b048698.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)
%e a(4) = 56: the aliquot divisors 1,2,4,7,8,14,28 sum to 64, a cube.
%p a := []; for n from 1 to 1000 do if sigma(n) <> n+1 and type( simplify((sigma(n)-n)^(1/3)), `integer`) then a := [op(a), n]; fi; od: a;
%t Select[Range[20000], !PrimeQ[#] && IntegerQ @ Surd[DivisorSigma[1, #] - #, 3] &] (* _Amiram Eldar_, Feb 23 2020 *)
%o (PARI) c=0; for(n=1, 13127239, if(isprime(n)==0, if(ispower(sigma(n)-n, 3), c++; write("b048698.txt", c " " n)))) /* _Donovan Johnson_, Mar 10 2013 */
%Y Cf. A020477, A048699, A194948.
%K easy,nonn
%O 1,2
%A _Enoch Haga_
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