A048698 Nonprime numbers k such that sum of aliquot divisors of k is a cube.

1, 10, 49, 56, 69, 76, 122, 133, 568, 578, 1001, 1018, 1243, 1324, 1431, 1611, 1685, 1819, 1994, 2296, 2323, 3344, 3403, 3627, 3641, 3763, 3981, 4336, 5482, 8186, 9077, 9641, 10113, 10688, 13471, 14188, 14509, 14727, 15940, 16697, 17141, 17619, 19241, 19637

Offset

1,2

Comments

The sum of the aliquot divisors of a prime is exactly 1. - Martin Renner, Oct 13 2011

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Example

a(4) = 56: the aliquot divisors 1,2,4,7,8,14,28 sum to 64, a cube.

Maple

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;

Mathematica

Select[Range[20000], !PrimeQ[#] && IntegerQ @ Surd[DivisorSigma[1, #] - #, 3] &] (* Amiram Eldar, Feb 23 2020 *)

Prog

(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 */

Crossrefs

Cf. A020477, A048699, A194948.

Sequence in context: A330170 A126734 A264266 * A045770 A217165 A154066

Adjacent sequences: A048695 A048696 A048697 * A048699 A048700 A048701

Keyword

easy,nonn

Author

Enoch Haga

Status

approved