A194948 -id:A194948 - cp's OEIS frontend

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

Enoch Haga

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

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

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

Cf. A020477, A048699, A194948.

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;

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

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 */

A244429 Nonprimes n such that the sum of proper divisors of n and the product of proper divisors of n are both perfect cubes.

Original entry on oeis.org

1, 56, 568, 1001, 1431, 3344, 10688, 17619, 24099, 37432, 40797, 46096, 50571, 52687, 55581, 62375, 75221, 88863, 97273, 98752, 111224, 134672, 235495, 247033, 251403, 266176, 269072, 271099, 275077, 299576, 320489, 333888, 364067, 372331, 407319, 534413, 561008, 614465, 646691

Offset: 1

Derek Orr, Jun 27 2014

nonn

Primes trivially satisfy this property and are therefore not included in this sequence.

These numbers are in the intersection of A194948 and A229972.

			The proper divisors of 56 are {1, 2, 4, 7, 8, 14, 28}. 1*2*4*7*8*14*28 = 175616 = 56^3. 1+2+4+7+8+14+28 = 64 = 4^3. Since both the product of proper divisors and the sum of proper divisors are cubes, 56 is a member of this sequence.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A244428, A064121, A229972, A194948.

for(n=1,10^7,d=divisors(n);s=sum(i=1,#d-1,d[i]);p=prod(j=1,#d-1,d[j]);if((p!=1||s!=1),if(ispower(s,3)&&ispower(p,3),print1(n,", "))))

cp's OEIS Frontend

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

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