A019422 Numbers whose sum of divisors is a fourth power.

1, 217, 510, 642, 710, 742, 782, 795, 862, 935, 1177, 1207, 1219, 2667, 3937, 7590, 7854, 8743, 9481, 9798, 9858, 10810, 10934, 11186, 11235, 11510, 11594, 11715, 11985, 12082, 12243, 12903, 12945, 13022, 13462, 13587, 13685, 13822, 14223, 15085

Offset: 1

Author

David W. Wilson

Keywords

• nonn

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 217, p. 62, Ellipses, Paris 2008.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• 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.

Programs

Mathematica

Select[Range[16000],IntegerQ[Power[DivisorSigma[1,#], (4)^-1]]&] (* Harvey P. Dale, Jan 22 2012 *)

PARI

c=0; for(n=1, 8240486, if(ispower(sigma(n), 4), c++; write("b019422.txt", c " " n))) /* Donovan Johnson, Jun 13 2013 */