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

1,2

Links

Michel Marcus, Table of n, a(n) for n = 1..40

Example

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.

Mathematica

q[k_] := And @@ IntegerQ /@ Sqrt[NumeratorDenominator[DivisorSigma[-1, k] - 1]]; Select[Range[2*10^6], q] (* Amiram Eldar, Apr 28 2025 *)

Prog

(PARI) isok(k) = issquare(sigma(k)/k - 1);

Crossrefs

Cf. A000203 (sigma), A069070.

Subsequences: A000396 (perfect numbers), A046060 (5-multiperfect numbers), A381321.

Cf. A218404 (for those terms with sigma(x)/x = 13/4).

Sequence in context: A025493 A368716 A091519 * A086491 A178597 A179908

Adjacent sequences: A383479 A383480 A383481 * A383483 A383484 A383485

Keyword

nonn

Author

Michel Marcus, Apr 28 2025

Extensions

a(30)-a(32) from Jinyuan Wang, Apr 28 2025

Status

approved