A019423 - OEIS

%I #34 Sep 08 2022 08:44:44

%S 1,21,31,651,889,3210,3498,3710,3882,3910,4310,4922,4982,5182,5457,

%T 5885,6035,6095,6307,6797,7117,7327,7597,24573,27559,71193,82110,

%U 90510,94981,97410,98671,99301,99510,100110,103362,104622,107778,108438,108822

%N Numbers whose sum of divisors is a fifth power.

%H Marius A. Burtea, <a href="/A019423/b019423.txt">Table of n, a(n) for n = 1..3648</a> (terms 1..1000 from Donovan Johnson; a(1211) re-indexed and duplicate a(2311) removed by _Georg Fischer_, Mar 21 2022).

%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.

%o (PARI) lista(nn) = {for (i=1, nn, s = sigma(i); if (s == 1 || ispower(s, 5), print1(i, ", ")););} \\ _Michel Marcus_, Jun 12 2013

%o (Magma) [n:n in [1..10000]| IsPower(SumOfDivisors(n),5)]; // _Marius A. Burtea_, Apr 17 2019

%Y Cf. A000203, A006532, A019422, A019424, A020477, A048257, A048258.

%K nonn

%O 1,2

%A _David W. Wilson_