A091287 Integer solutions x to (sigma(x)+sigma(x+1))/sigma(2*x+1), where sigma() = A000203.

1, 4, 215, 646, 923, 944, 1096, 1715, 2379, 5355, 16174, 22891, 38429, 64672, 87584, 110483, 212795, 291039, 353110, 468970, 515698, 733570, 1016519, 1051644, 1198139, 1317343, 1633213, 1735288, 2026945, 2093506, 2709542, 2729979

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..200

Example

n=215, sigma(215)+sigma(216) = 264+600 = 2*432 = 2*sigma(215+216) = 2*sigma(431).

Mathematica

Do[s=(DivisorSigma[1, n]+DivisorSigma[1, n+1])/ DivisorSigma[1, 2*n+1]; If[IntegerQ[s], Print[n]], {n, 1, 10000000}]
Position[Table[(DivisorSigma[1, n]+DivisorSigma[1, n+1])/DivisorSigma[ 1, 2n+1], {n, 28*10^5}], _?IntegerQ]//Flatten (* Harvey P. Dale, Nov 24 2017 *)

Prog

(PARI) is(n)=(sigma(n)+sigma(n+1))%sigma(2*n+1)==0 \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A000203, A067171, A091290.

Sequence in context: A340176 A038790 A042325 * A338282 A281997 A276487

Adjacent sequences: A091284 A091285 A091286 * A091288 A091289 A091290

Keyword

nonn

Author

Labos Elemer, Feb 16 2004

Status

approved