A019423 Numbers whose sum of divisors is a fifth power.

1, 21, 31, 651, 889, 3210, 3498, 3710, 3882, 3910, 4310, 4922, 4982, 5182, 5457, 5885, 6035, 6095, 6307, 6797, 7117, 7327, 7597, 24573, 27559, 71193, 82110, 90510, 94981, 97410, 98671, 99301, 99510, 100110, 103362, 104622, 107778, 108438, 108822

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..3648 (terms 1..1000 from Donovan Johnson; a(1211) re-indexed and duplicate a(2311) removed by _Georg Fischer_, Mar 21 2022).
• 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, A019424, A020477, A048257, A048258.

Programs

Magma

[n:n in [1..10000]| IsPower(SumOfDivisors(n),5)]; // Marius A. Burtea, Apr 17 2019

PARI

lista(nn) = {for (i=1, nn, s = sigma(i); if (s == 1 || ispower(s, 5), print1(i, ", ")););} \\ Michel Marcus, Jun 12 2013