A383482 Integers k such that sigma(k)/k - 1 is a rational square.
1, 6, 9, 28, 216, 360, 496, 2016, 2401, 8128, 16758, 182520, 884736, 1022112, 1352328, 1571328, 1935360, 2678400, 33550336, 54758400, 101382400, 119533176, 136808280, 163298502, 198288000, 618591192, 691022088, 782481673, 796663296, 1137067008, 1275418369, 1303102080
Offset: 1
Keywords
Examples
6 is a term because sigma(6)/6 - 1 = 2 - 1 = 1, a square; like for all perfect numbers. 9 is a term because sigma(9)/9 - 1 = 13/9 - 1 = 4/9, a square.
Links
- Michel Marcus, Table of n, a(n) for n = 1..40
Crossrefs
Programs
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Mathematica
q[k_] := And @@ IntegerQ /@ Sqrt[NumeratorDenominator[DivisorSigma[-1, k] - 1]]; Select[Range[2*10^6], q] (* Amiram Eldar, Apr 28 2025 *)
-
PARI
isok(k) = issquare(sigma(k)/k - 1);
Extensions
a(30)-a(32) from Jinyuan Wang, Apr 28 2025