A019424 Numbers whose sum of divisors is a sixth power.

1, 2667, 3937, 17490, 19410, 22578, 24610, 24910, 25466, 25910, 26554, 26818, 27285, 29342, 29733, 29762, 31102, 31535, 32043, 32997, 33985, 35585, 36635, 37985, 39697, 41393, 41837, 42347, 44047, 45637, 45739, 45937, 46117, 172011, 253921, 640737

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Examples

			sigma(2667) = 1+3+7+21+127+381+889+2667 = 4096 = 4^6.
sigma(3937) = 1+31+127+3937 = 4096 = 4^6.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..2010 (terms 1..1000 from Donovan Johnson)
• Frits Beukers, Florian Luca and Frans Oort, Power Values of Divisor Sums, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.

Crossrefs

Cf. A000203, A006532, A019422, A019423, A020477, A048257, A048258.

Programs

Magma

[n:n in [1..100000]| IsPower(SumOfDivisors(n),6)]; // Marius A. Burtea, Apr 17 2019

Mathematica

Select[Range[700000],IntegerQ[Surd[DivisorSigma[1,#],6]]&] (* Harvey P. Dale, Apr 19 2019 *)

PARI

c=0; for(n=1, 306455560, if(ispower(sigma(n), 6), c++; write("b019424.txt", c " " n))) /* Donovan Johnson, Jun 13 2013 */