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 A048698 Nonprime numbers k such that sum of aliquot divisors of k is a cube. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified October 28 04:06 EDT 2020. Contains 338048 sequences. (Running on oeis4.)