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

1,2

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.

Example

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

Mathematica

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

Prog

(PARI) c=0; for(n=1, 306455560, if(ispower(sigma(n), 6), c++; write("b019424.txt", c " " n))) /* Donovan Johnson, Jun 13 2013 */
(Magma) [n:n in [1..100000]| IsPower(SumOfDivisors(n), 6)]; // Marius A. Burtea, Apr 17 2019

Crossrefs

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

Sequence in context: A187195 A107532 A110838 * A151813 A010088 A252301

Adjacent sequences: A019421 A019422 A019423 * A019425 A019426 A019427

Keyword

nonn

Author

David W. Wilson

Status

approved