%I #29 Sep 08 2022 08:44:44
%S 1,2667,3937,17490,19410,22578,24610,24910,25466,25910,26554,26818,
%T 27285,29342,29733,29762,31102,31535,32043,32997,33985,35585,36635,
%U 37985,39697,41393,41837,42347,44047,45637,45739,45937,46117,172011,253921,640737
%N Numbers whose sum of divisors is a sixth power.
%H Marius A. Burtea, <a href="/A019424/b019424.txt">Table of n, a(n) for n = 1..2010</a> (terms 1..1000 from Donovan Johnson)
%H Frits Beukers, Florian Luca and Frans Oort, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.05.373">Power Values of Divisor Sums</a>, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.
%e sigma(2667) = 1+3+7+21+127+381+889+2667 = 4096 = 4^6.
%e sigma(3937) = 1+31+127+3937 = 4096 = 4^6.
%t Select[Range[700000],IntegerQ[Surd[DivisorSigma[1,#],6]]&] (* _Harvey P. Dale_, Apr 19 2019 *)
%o (PARI) c=0; for(n=1, 306455560, if(ispower(sigma(n), 6), c++; write("b019424.txt", c " " n))) /* _Donovan Johnson_, Jun 13 2013 */
%o (Magma) [n:n in [1..100000]| IsPower(SumOfDivisors(n),6)]; // _Marius A. Burtea_, Apr 17 2019
%Y Cf. A000203, A006532, A019422, A019423, A020477, A048257, A048258.
%K nonn
%O 1,2
%A _David W. Wilson_
|