OFFSET
1,3
COMMENTS
It is conjectured that only 1 and 1782 satisfy a(x) = 0.
REFERENCES
R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third Edition, 2004, B11.
LINKS
Michel Marcus, Table of n, a(n) for n = 1..10000
K. Broughan, J.-M. De Koninck, I. Kátai, F. Luca, On integers for which the sum of divisors is the square of the squarefree core, J. Integer Seq., 15 (2012), pp. 1-12.
Yong-Gao Chen, and Xin Tong, On a conjecture of de Koninck, Journal of Number Theory, Volume 154, September 2015, Pages 324-364. Beware of typo 1728.
MAPLE
a:= n-> mul(i[1], i=ifactors(n)[2])^2-numtheory[sigma](n):
seq(a(n), n=1..60); # Alois P. Heinz, Nov 09 2020
PROG
(PARI) a(n) = my(f=factor(n)); factorback(f[, 1])^2 - sigma(f);
CROSSREFS
KEYWORD
sign
AUTHOR
Michel Marcus, Nov 09 2020
STATUS
approved